Hello everyone, welcome to the new video.
In this video, we will check divisibility.
When is a number divisible by any other number?
We will see the test for that.
Before checking divisibility, we should know what is
divisible?
Why do we say it is divisible or not?
What is divisible?
What is divisible by 2 or 4?
If we are checking a number from 2, when will it be
divisible by 2?
When is it being divided by 2?
Is it a multiple of 2?
When is it being divided by 2?
I have taught you what is a multiple of 2.
So, if we have any number from 2 or 4 which is divisible or
not we will check whether it is being divided by 2 or is it
a multiple of 2?
So, this is the meaning of divisible.
Now, we will check the test for any particular number.
We have tests for numbers from 2 to 19.
1 is not divisible because 1 is as usual.
Every number is divisible by 1.
We have tests for numbers from 2 to 19.
We will learn that in today's class.
So, let's start with the easiest one.
We will start with 2.
I have made some groups of the same type of tests.
All of them are in one slot.
The rest are in different groups.
In the first group, we are doing 2, 4, 8, 16.
To check these, let's start with 2.
For 2, most of the students will know that the definition
of even number which we had studied earlier is the same as
the definition of even number.
So, we will check whether any number is divisible by 2 or
not.
To check whether any number is divisible by 2 or not, we
have to check its unit place.
Unit place means the first digit.
So, the unit place will be the last digit.
What do we call the last digit?
We call it the unit place digit.
It should be either 2, 4, 6, 8 or 0.
2, 4, 6, 8 are all even numbers.
The rest are 0.
0 is neither odd nor even.
But, as we can see, we include 0 in the unit place.
If any digit is present in the unit place, then that digit
will be divisible by 2.
Next, let's check 4.
For 4, we have to check the last digit.
For 4, we have to check the last two digits.
The last two digits are 8, 2, 4, 6.
So, what are the last two digits? 4, 6, 46.
Does 46 come in the table of 4?
Does 46 come in the table of 4 or not?
What is 4 into 11?
It is 44.
So, does 46 come in the table of 4 or not?
The last two digits are not divisible by 4.
So, this whole number 8, 2, 4, 6 will also not be divisible
by 4.
Let's check 8, 2, 6, 4
Does it come in the table of 4 or not?
Is it divisible by 4?
First, we will check the last two digits of this number.
What is 64? 64 comes in the table of 4.
64, 4, 1.
16, 4.
So, this whole number is divisible by 4.
That is 64.
So, this whole number 8, 2, 6, 4 will also not be divisible
by 4.
Now, we will move on to the next digit.
That is 8.
For 2, we will check the last two digits.
For 8, we will check the last three digits of the number.
We will check the last three digits of the number.
Is it divisible by 8?
If it is divisible by 8, then the whole number will be
divisible by 8.
Otherwise, it will not be divisible by 8.
For 16, we will check the last four digits.
If the last four digits are divisible by 16, then the whole
number is divisible by 16.
If the last four digits are divisible by 16, then the whole
number is divisible by 16.
So, now you can understand the rest of the numbers.
It is very simple.
Next, we will move on to the next group.
That is 3.
We will check the last four digits.
For 3, 9, and 11.
Before 3, 9, and 11, I will show you another example.
Let's check 5 and 10.
5 and 10 are also very simple.
If we want to check any number for 5, we will check the
last digit of the number.
That is the last digit of the number.
The last digit of the number should be either 5 or 0.
If any of these two digits are in the last digit, then the
number will be automatically divisible by 5.
then the number will be automatically divisible by 5.
If you observe in the table of 5, the last digit of the
number is either 0 or 5.
There should be no other digit.
But for 10, there should be only one digit.
That is the last digit of the number.
There should be no other digit.
Then we can say that the number is divisible by 10.
So, we have checked 2, 4, 8, 16, 5, and 10.
Now moving on to the next group.
The next group is 3, 9, and 11.
3 and 9 are different from 11.
But I have put them in the same category.
Because we are adding and subtracting with the digits.
I will tell you what to do in 11.
So, what will happen to 3? We have given any number in the
table.
So, we have to add all the digits.
And the result we get after adding the digits, if it is
divided by 3, then we will say that the number is divisible
by 3.
Otherwise, it is not divisible by 3.
For example,
Suppose we have a 5 digit number.
We have to check whether it is divisible by 3 or not.
So, we have to check whether it is divisible by 3 or not.
If I add all the digits, Then we get 8 plus 6.
14 plus 1 is 25 and 25 plus 9 is 14, 8 plus 6 is 14, 14
plus 1 is 15 and 15 plus 9 is 24.
Can we write 24 in multiple of 3?
Obviously, 24 is 3 into 8.
3 x 8 is 24.
So, if we have the sum of multiple of 3, then we can say
that the whole number 17691 is divisible by 3.
Now, let us write 9.
What is 9 for 3?
We should have the sum of multiple of 3.
What is 9 for 3?
We should have the sum of multiple of 9.
If we are checking for 9, then we should have the multiple
of 9.
If we are checking for 3, then we should have the multiple
of 3.
So, the multiple of 3 should be 9.
Now, let us check the question.
If we have the question 6, 7, 3, 5, 6.
This is also a 5 digit number.
If we are checking for 9, then we should have the multiple
of 9.
So, how will we do it?
We will sum all these digits.
And we will check whether it is the multiple of 9.
So, what will be the sum of all these digits? 6 plus 7 is
13.
13 plus 3 is 16.
16 plus 5 is 21.
21 plus 6 is equal to 27.
And what is 27? 9 into 3.
9 into 3 is equal to 27.
So, the multiple of 9 is 27.
So, the whole number 6, 7, 3, 5, 6 is also the multiple of
9.
That is, it is divisible by 9.
This is the answer in the table of 9.
The answer of 9 is same as the answer of 3.
Now, let us check the answer of 11.
This is something different.
11, 9, 3, 5, 6, 7, 8, 9.
It is a bit different.
Let us see the answer of 11.
Here, we have a number 5, 1, 1, 5.
We have got a number 5, 1, 1, 5.
This is a positive number.
Now, let us see the answer of 11.
The answer of 11 is an alternative number.
What does alternative mean?
This means that after one gap between digits, let us keep
one minus the other.
Alternatively, we will write plus here.
In English, we can write the answer as
I will explain to you that we have this, give them that,
give them the address, like if this is on 1st place, this
is 2nd, this is 3rd, this is on 4th place, you can start
the numbering like this, you can start from that side too,
there will be no difference
in that.
If we have done this, okay, so this number is on even
places, even places means where there is an even address,
so where is the even address?
This 2 and this 4, we have to sum them together.
In this, what we were doing in 3 and 9, we were not looking
at the address, what we were doing is, we were adding all
the digits by taking them straight.
But in this also, we will do, but what will we add?
The pattern of adding will be different, that is, we will
not add all of them together, we will make a pair or a
couple of particular things or whatever group we make, we
will add that.
So, like this is even places, 2 and 4 are even places, the
digits coming on them, even places, digits at even places,
what is that?
One is 5, this is on 4th and this is 1, this is on 2nd
place, so we will sum them.
Sum of digits at even places, so what is this 5 plus 1? 6.
Similarly, we will get the second sum, sum of digits at odd
places.
What are the odd numbers? 1 and 3, what is the number on
that address? 5, 5 from here and 1 from here.
So, 5 plus 1, what is this? 6.
So, we got the sum of the digits at even places and the sum
of the digits at odd places.
Now, what will we see after this? After this, whatever sum
of even and odd places we got, what will we do to these
two? We will subtract and after subtracting, what will be
our answer? In this, we were looking at multiple of 9 or 3,
what should be there
in this?
Either, the difference between them, difference, the
difference between these two,
The difference between the sum of even and odd places, if
we get either 0 or 11 or the multiple of 11.
So, what will we say? We will say that that number is
divisible.
What will be the difference?
What is the difference between the sum of odd places and
the sum of even places?
If we get the difference of 0 or 11, then we will say that
the whole number is divisible by 11.
Like, what was there in this? We got the sum of 6.
The sum of even places was 6 and the sum of odd places was
6.
So, what will be the difference of both?
What will be the difference? 6 minus 6, that is 0.
So, there is 0 in this.
In the option, there should be 0 or 11.
So, we got 0, that is 5, 1, 1, 5.
What is this number? It is divisible by 11.
You can check this and see if it is divisible by 11.
This will happen because our test says that it will happen.
You can check for your satisfaction and see if it is
divisible by 11 or not.
Then you will believe more in what ma'am said.
And until you believe in what you are studying in Maths or
any other subject, you will not be able to keep the desire
to learn it or you will not be able to make an interest in
it that we should learn this more.
That will be written.
So, gradually understand yourself, verify yourself and
practice.
The more questions you practice, the more your speed will
increase.
You will be more confident about a particular topic.
Now, see these questions about divisibility.
These questions will not come directly.
But, it will be helpful for your questions or for any other
calculation.
So, what is this? This is not a question.
These are tools.
Tools to solve those bigger problems.
To solve any complex problem, how do we solve the bigger
problem?
We segregate it.
We divide it into small pieces.
And then we solve those small pieces slowly.
Then we reach the final answer.
Then we solve the bigger problem.
So, this is also a tool for you to solve the bigger
questions.
I hope you have understood the answers of 3, 9, 11, 5, 10,
2, 4, 8 and 16.
Now, let's see the remaining answers.
We are doing till 2 to 19.
Now, let's see the remaining answers.
Next, we have divisible by 6, 12, 14, 15, 18.
Why have I kept all these in one category?
Let me tell you.
What do we have to check in these?
There is no rule in these.
We will check these in the factor.
You have read the factor, multiple and factor.
Factor means in which table these come.
For example, 6.
In which table does it come?
It comes in 1, 2, 3 and 6 tables.
So, the factors of the table in which it comes.
And whatever comes in this table, like 6, 12, 18 and so on.
These are called multiples.
We are checking multiples in this.
Divisibility is checking multiples only.
So, what will help us?
We will get the help of factors for these 5 cases.
We will break them in factors.
And those factors will break in small numbers.
Which we have done till 1 to 10.
Then we will see from them.
Will they be solved?
Will we be able to see them or not?
So, suppose I told you about 6.
So, if I told you about 6.
I will erase this.
If we factor 6.
So, what can we do in the factor of 6? 6 is equal to?
We can write 6 as 2 into 3.
Both are prime numbers.
So, if any of our numbers which we have been asked.
Is it divisible by 6 or not?
So, what we will see?
If it is 2 and 3.
AND means?
In AND, we have to write both of them.
If the given number is divisible by 2 and 3 both, then we
will say that number will be divided by 6.
If a number is coming in the table of 2 and 3, then
obviously it will come in the table of both.
It is not like that it is coming in the table of 2 and 2
only.
Like 4 is coming in the table of 2 and 2 only and not in
the table of 3.
So, 4 will not be divisible by 6.
But suppose 12 comes in the table of 2 and 3, then 12 will
be divisible by 6.
And obviously 12 is divisible by 6.
6x2 is 12.
So, it should come in the table of both.
So, this is important.
Both.
Both word is very important.
So, 2 and 3 should come in the table of both.
Similarly, how can you divide 12?
You can divide 12 by 4x3.
So, if the given number is divisible by 4 and 3 both,
If the given number is divisible by 4 and 3 both, then we
can directly say that it is divisible by 12.
14.
How can we factorize 14? 2x7.
So, 7.
We have not studied the divisibility test of 7.
I will tell you that next.
But for now, understand that the number should come in the
table of 2 and 7.
And it should also come in the table of 7 and 6.
So, it will automatically be divisible by 14.
14 will also come in the table.
So, what is the rule for 14? 2 and 7 both.
Divisible by 2 and 7 both.
What will happen for 15?
Factorize 15.
What will happen to 15? 3x5.
So, what will happen? 3 and 5 should come in the table of
both.
Means, the number should be divisible by both.
So, this number will also be divisible by 15.
Similarly, what will we write for 18? 2x9.
So, what should happen to 2 and 9?
That number should be divided.
So, it will automatically be divisible by 18.
Whatever we have done so far, understand that it is easy.
It is not very tough.
Now, if you say something tough, it will not be tough when
we do next.
If you practice, it will not be tough.
But it will be a little new.
Our steps will increase in it.
So, we will get that.
That is the chart number.
What is left from 2 to 19? One is 7 from 1 to 10.
7 was left.
Then 11 and 12 were left.
Then 13 was left.
Then 14 and 15 were left.
16 was left in the previous group.
17 was left.
Then 18 and 19 were left.
So, we have 4 such numbers left.
We have to check the divisibility of these numbers.
And they will be slightly different from this.
Means, it will be a little more calculative than this.
So, if you practice it, you will get those tips.
Means, your hand will move fast.
Maths is the same.
The more time you give it, the more you will understand it.
There was a dialogue in it.
Girlfriend is like any other subject.
The more time you give it, the more it will get attached to
you.
So, every subject, not only maths, every subject or every
thing for which you are dedicated, they will apply for it.
Whatever you give more time, obviously, it will be good for
you.
There are exceptions in it.
But, most of the time, you will get good results in
everything.
Next, see, a little tough one.
Take a little breath before tough.
Because, this will be a little different from all of them.
If you are starting from here,
So, first, take a pause here and revise all of them.
Then, see it with a fresh mind, that how we will do this.
Drink water, do everything.
Then, we will see divisibility of 7, 13, 17 and 19.
I have written the direct question of this.
Because, you will understand it faster with the question.
So, we will see 7.
What do we have to do for 7?
For example, I have written 7, 13, 17 and 19.
So, put a sign in front of 7.
Put a minus in front of 7.
Put a plus in front of 13.
Put a minus in front of 13.
Put a plus in front of 13.
Alternative sign.
You will get to know it gradually, why ma'am has put such a
sign here. So, we will check 7.
How will we check for 7?
Suppose, we have a question.
3, 2, 0, 4, 6.
Is it divisible by 7 or not?
How will we check it?
We will check it.
First of all, we will take the digit of unit place.
We took the last digit.
6.
We took the last digit.
Take 6.
Separate 6 and 3, 2, 0, 4.
So, we have written 3, 2, 0, 4 separately.
We have taken 6 separately.
Separate it.
So, what we have to do for 6?
We have to multiply 6 by 2.
Which means, the digit of unit place, we have to multiply
it by 2.
We have to multiply it.
Now, what will be the answer for 6? 12.
So, subtract 12 from the remaining part.
So, we will do minus.
So, we have done minus 12.
What will be the answer for 4? 4 minus 2 is 2.
Here, we will take 10 minus 1 is 9.
Here, 1 is left.
1, 3, 1, 9, 2.
Now, this is also a 4 digit number.
This is also big.
So, as this was 4 digit from 5 digit.
See, it is 4 digit.
Similarly, we will make it smaller.
So, see, do the same process.
Repeat it.
What was the last step?
We took the digit of last unit place.
Now, we have the result.
3, 1, 9, 2.
What was the last digit?
We took 2 separately.
We wrote 3, 1, 9 and 2 separately.
Then, how to multiply it?
We have to multiply it by 2.
So, we will multiply 2 by 2.
What is this? 4.
Then, what to do with 4?
See, here was the sign of minus.
We did minus.
So, what to do with 4?
Subtract the remaining portion.
So, what is this? 3, 1, 9, minus 4, 9, minus 4, 5.
So, this is 3, 1, 5.
See, first it was 5 digit.
Then, 4 digit was left.
Now, 3, 1, 5 is left.
That is 3 digit.
Then, continue this step.
What was the last digit?
We had to take the last digit.
What was the last digit?
We had to multiply it by 2.
So, this is 10.
Now, what to do with 10?
Subtract the remaining portion.
What is this? 21.
Now, 21 is here.
What did we see in 21?
We saw clearly that it comes in the table of 7.
7, 3's are 21.
So, if we follow this step, the last digit or the small
digit or you can see it on 3, 1, 5.
You can stop it anywhere.
But, if you come to know that it is a multiple, then you
can stop it there.
No problem.
For example, I stopped at 21.
I stopped at 21.
So, I got 21.
This is a multiple of 7.
So, as soon as we follow this step, we get a multiple of
that number.
If we check 7, if we get a multiple of 7, or 7, then we
will say that this whole number, 3, 2, 0, 4, 6, this whole
number is divisible.
by 7 here.
Did you understand?
Let me explain it again in short term.
What we will do is we will see the last digit number.
We will see the last digit number.
In that we will do multiply 2.
So, if we multiply 2,
I have put minus sign here.
So, I will put into 2 in the bracket.
So that you can remember it at one place.
We will put into 2.
And whatever result will come, we will minus it from the
remaining digits.
We will remove the remaining number 6 and we will minus it.
Then the answer will come.
In that we will follow those steps again till we get a
small number which is a multiple of 7.
If it is a multiple of 7, whatever is remaining in the last
digit, then we will say that it is divisible by 7.
Otherwise, it is not.
Did you understand this much?
So, this will be your homework.
For 7, I have told you this.
If you did not understand, then see it again.
Listen to my steps again.
And then try this.
First try this.
After seeing my steps.
Then try this.
And see whether it is a multiple of 7 or not.
After 7,
I have written 13.
So, I have put plus sign for 13.
So, how will we do 13?
We have been given a question.
1110526 Will this number be divisible by 13 or not?
So, what will we do in this?
In that, we did into 2.
See, we did into 2.
In this, we will do into 4.
I will write it here.
In this, we will do into 4.
How will we multiply unit place?
We will do into 4.
And then, what will we do in remaining?
We will do into plus sign.
In 7, we were subtracting.
Because it was minus sign.
In 13, we will do plus sign.
Let me show you the question.
First, see the unit digit.
What is the unit digit?
It is 6.
How will you multiply it?
Now, write 6 separately.
And write remaining numbers separately.
How will we multiply 6?
We will multiply it by 4.
What will be 6 times 4? 24.
What will we do with this number?
See the sign.
I have written plus.
What will we do with it?
We will do plus in this number.
Whatever we have multiplied, we have to add it.
So, we will add 24.
What is it? 67011.
Still, it is a big number.
How much?
It is a 5 digit number.
From 6, it is 5 digit.
So, the same procedure, which we did in the last, we
repeated the same process.
Till we get a small number.
We will repeat the same process again.
What will we do?
We will multiply 6 by 4.
Write 6 and 4 together.
And write 6 separately.
So, we had to multiply 6 by 4.
We multiplied it by 4.
Then, we got 24.
What will we do with 24?
We have to add it.
So, plus 24.
What is it? 111311.
Still, it is a big number.
It is a 4 digit number.
We will make it smaller.
Then, we will repeat the same process.
What will we do with the last digit?
We will multiply it by 4.
So, 1x4 is 4.
What will we do with the remaining digits?
We will add it.
So, what is this plus 4? 11711.
11711 is done.
Then, you can directly divide it by 13.
So, will it come in the table?
Will it come in the table of 13 or 117? 117.
13x9. 13x9.
9x3 is 27. 9x1 is 9.
11. 117.
So, what is this? 13x9.
We got the multiple of 13.
If we get the multiple of 13, we will stop here.
What will we call it?
This is divisible.
This is the whole number.
11110526.
This whole number is divisible by 13.
You have a homework for this also.
First, understand this well.
Solve it by yourself.
Then, do this homework.
And, tell us.
Comment and tell us what is your answer.
Check whether it is divisible by 13 or not.
So, we got 11.
We got 13.
Then, it was 17. So, in 17, there is a minus sign.
Now, it was x2 and x4.
What will be x5 in this?
It will be same as 7.
In 7, we were doing x2.
In this, we are doing x5.
Let's do a question of 17.
So, what will we do?
Tell us.
We have to multiply the last digit by 5.
How to do it?
I have just told you.
We have to multiply it by 5.
How to do it?
We have to multiply it by 5.
What else we have to do?
Look at the sign.
I have put a minus sign on 17.
So, what will we do?
We have to multiply it by 5.
We will minus it.
It is 6.
It is the last digit.
We have taken 6.
We have written it separately.
What will we do with 6?
We have to multiply it by 5.
It is 30.
We have to minus 30.
What was the sign?
It was a minus sign.
We have to minus 30.
What is left? It is 11101.
Follow the same step.
Take the digit of unit place.
Multiply it by 5.
And subtract the remaining digit. It is minus 5.
What will it be? 10 minus 5 is 5.
It is 01105.
Follow the same step.
Take the digit of unit place.
What did we do?
We multiplied it by 5.
And what did we do with the remaining digit?
We minus it.
It is 5.
2 out of 10 is 8.
It is 85.
Normally, you can check it from 17.
It is 5.
Multiply it by 5.
It is 17 into 5.
It is 35.
5 into 1 is 85.
What can we write for 85?
It is 17 into 5.
It is 17.
It is a multiple of 17.
The whole number will be divisible by 17. It will be.
It is similar to 7.
Now, this is your homework question.
Homework question.
It is 93194.
934.
We have 17.
18.
We have 18.
Now, the last one is 19.
I have also written 19 in this group.
What is the sign in that group? It is plus.
We will multiply it by 2.
We will multiply unit place by 2. We multiplied 7 by 2.
We multiplied 7 by 2.
But, we had put minus sign in 7.
We were putting minus sign.
There is a plus sign in 7.
We will multiply 2 by 2.
We will put plus sign in remaining.
What is the plus sign?
It is like we did in 13.
Let us see the question of 19.
Let us see.
We have a question.
Is 9652 divisible by 19?
What to do?
Multiply by 2 and plus.
Place by 2.
2 to the side.
965 to the other side.
How to multiply 2?
Multiply by 2 for 19.
2 into 2.
4.
What to do to 4?
What do you do with this?
Add it.
Plus sign was there for 19.
So add it.
9654 plus 965 plus 4.
So what is the answer? 969 Now how will we solve this?
Again the same thing.
Continue the same step.
Take the last digit.
9 Write 9 separately.
How to multiply 9?
By 2.
So multiply by 2. 18. 18 ko ab kya karna hai? Add karna hai
isme.
To plus 18 yeh kya aagaya? 6 plus 8, 14, 1.
That is 114.
Aap dekhi kya 114 humara 19 se ja rahe hai? 19 ki table
mein aata hai? 4 ka baat hai? 6 za? Ek baad 6 se karte hain.
19 into 6? 9 za? 54.
6 ones a 6? 11.
To humare paas dekho 114 ja rahe hai.
114 ko kya likh sakte hain hum? 19 into 6.
To yeh 19 ka multiple aagaya.
19 ke liye hi hum check kar rahe the.
Agar jis ke liye hum check kar rahe hain, usi ka multiple
wo sare steps karke aagaya.
To hum kya kahenge? Yeh poora ka poora number divisible by
19 hai.
To I hope aapko yaha tak sare yeh 1 se lekar 19 tak sare
samajh aagayi hunge.
19 ke liye yeh homework likhe aap logon ke liye 21812.
Yeh aapko check karna hai.
Isme aapko koi dikkat nahi hone chahiye.
Agar phir bhi aapko koi dikkat hogi, to aap bhi ek baad
dubhara se dekh lena yeh steps ke maine kya kiye hain, aur
phir thode se questions aur practice kar lena.
Jitni zyada practice karoge, utne zyada jaldi yeh solve
honge aur aapko practice bani rahegi.
Nahin to aap yeh bhool jayenge.
Ek question karne ke baad aap yeh bhool jayenge.
Isliye aapko inko routine milana padega.
To thank you ab milenge next video me.
Spread the word to all my friends.