Question

If a number is divisible by 8, then it is also divisible by 4 also. Explain?

Answer 1

Hint:In the given question, we have been asked that if a number is divisible by 8 then it is also divisible by 4 also. Here, we use the concept of factors. If any number is divisible by 8 and we know that 4 is the factor of 8, then the number is divisible by 4 also.

Complete step by step solution:
Let’s suppose a number ‘A’ be divisible by 8.
If any number is divisible by 8 then it must contain 8 as a factor.
Thus, \[\Rightarrow A=8\times B\] , where ‘B’ is the number that is the result when A is divided by 8.
Now,
We saw that 8 is the factor of a number ‘A’ and
We know that,
\[\Rightarrow 8=2\times 4\] that means 4 is a factor of 8.
Now, a number ‘A’ can be written as,
\[\Rightarrow A=8\times B\]
\[\Rightarrow A=2\times 4\times B\]
Therefore, if any number is divisible by 8 or 8 is a factor of any number and 4 is a factor of 8, then that number is divisible by 4 also.
So, a number ‘A’ is divisible by 4 also.

Note: We can also check if a number is divisible by 4 in another way also i.e. by using the divisibility of 4. Divisibility of 4 says that if the last two digits of any number is divisible by 4, then the whole number is also divisible by 4. For example; let’s take a number 780, the last two of this number is 80 and we can see that the number 80 is divisible by 4 i.e. \[80=4\times 20\]. So therefore, the whole number 780 is divisible by 4.