In this video, we learn a very important technique to check whether a given number is divisible by
a composite number.
All right.
Let's quickly think of what we have learned so far.
We have learned that there was a bullet holes four to four and eight.
We have also learned the rules for three and nine, and we have learned the rules for five and 10.
All right.
Now, over here we have six.
Six is a composite number, right?
It's not a prime number.
Therefore, it is a composite number.
All right.
Now, if I want to check whether a given number is divisible by a composite number, I need to express
the composite number as a product of.
Go prime numbers.
What do I mean with prime numbers, these are numbers which have no other common factor other than one.
All right, well, let me express six as six is equal to two and three.
And with this example, we'll understand this in a better manner to I am writing six as two into three.
Now, if a number is divisible by two and three, it's divisible by six.
For example, let's take the number four.
Ninety eight, we can see that the digit is eight.
Therefore it's divisible by two.
Right.
We have learned the divisibility rule of tool and what's the digit some over here or plus nine is 13,
13 plus eight is twenty one.
Twenty one is divisible by three therefore or four nine.
Eight is divisible by three therefore because four nine eight is divisible by two and four nine, eight
is divisible by three.
Therefore we can see that four ninety eight is divisible by six.
Now remember we were here two and three have no common factor other than one.
When we make some space over here.
The important thing that you need to keep in mind when applying this principle is we over here two and
three have no common factor.
Other than one and this type of numbers, that is, you have two numbers which have no common factor
other than one, these are called call prime numbers.
So they are there.
They don't need to be necessarily prime, for example.
Twenty five and sixty four, you know, twenty five is not a prime number.
It's five square and sixty four is eight squared.
That's also not a prime number, but twenty five and sixty four have no common factor.
Or the SCAF of twenty five and sixty four is equal to one because there's no common factor to twenty
five and sixty four are an example of prime numbers.
All right, now let's move on.
Let's take one more example so that you understand this very well.
Say you want to check whether a given number is divisible by twelve.
All right.
Now I can write 12 as six in the two or I can write 12 as four and three.
Now you need to know that checking whether the given number is divisible by six and whether the given
number is divisible by two is not sufficient to establish that the given number is divisible by 12.
Let's take an example.
Say you have the number six.
Six is divisible by six.
Yes, six is divisible by two.
Yes, but six is not divisible by twelve right now.
This is not this has not worked because two and six are not.
There is a common factor of two, right, but these are not cooperating.
So this is not sufficient to establish whether the given number is divisible by 12.
All right.
Now, when it comes to foreign trade, it is sufficient because four and three are prime numbers.
So what do I mean when I say it's sufficient that we make some space over here?
To check the divisibility by 12, the given number has to be divisible by or and it has to be divisible
by three.
If that is satisfied, the given number is divisible by 12.
Let's, for example, construction number that will be divisible by 12.
I know four divisible by for the last two digits have to be divisible by four.
Let me keep it as forty four.
I know that forty four is divisible by four.
Right.
OK, now if I want a number to be divisible by three, the sum of the digits has to be divisible by
three.
Over here I have four plus four.
That's eight.
Now if I add one to it or plus four plus one that's nine.
Right.
Or the this number over here is divisible by three and this number is divisible by four.
Therefore this number will be divisible by twelve.
And you can see one forty four is nothing but twelve in the twelve and hence one forty four is divisible
by twelve.