Q1. You have seen that a number 450 is divisible by 10. It is also divisible by 2 and 5 which are factors of 10. Similarly, a number 135 is divisible 9. It is also divisible by 3 which is a factor of 9.
Can you say that if a number is divisible by any number m, then it will also be divisible by each of the factors of m?
Yes, it has been proved that if a number is divisible by any number m, then it will also be divisible by each of the factors of m.
Let's Assume n is divisible by m, and m is divisible by k.This means
n=pm and
m = qk where all are integers
Now,
n = p(qk) =( pq)k which means n is divisible by k.
Hence a number is divisible by any number m, then it will also be divisible by each of the factors of m.