Prove that:`33!` is divisible by `2^15`.

Find the least number greater than 400 which is divisible by 12, 15.

Using binomial theorem prove that 4^n -3n-1 is divisible.by 9 for n in N

Prove that the product of two consecutive positive integers is divisible by 2.

Find the smallest square number that is divisible by each of the numbers 8,15 and 20.

For n in N prove that 5^n+2.3^(n-1)+1 is divisible by 8.

What is cell division?

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 by 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?

Prove by mathematical induction 2^(3n)-1 is divisible by 7.

Find the sum of first 15 positive integer which are are divisible by 8.

(n^2-1) is divisible by 8,if n is