Show that product of any n consecutive integers is always divisible by n!

The product of n consecutive natural numbers is always divisible by

True or false: The product of any r consecutive natural numbers is always divisible by r!

Prove that the product of three consecutive positive integers is divisible by 6 .

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

The product of three consecutive numbers is always divisible by 6. Verify this statement with the help of some examples.

Statement-1: The smallest positive integer n such that n! can be expressed as a product of n-3 consecutive integers, is 6. Statement-2: Product of three consecutive integers is divisible by 6.

Prove that the sum of two consecutive odd numbers is always divisible by four.

Statement-1: n(n+1)(n+2) is always divisible by 6 for all n in N . Statement-2: The product of any two consecutive natural number is divisible by 2.

5^(n)-1 is always divisible by (n in N)

The product of any three consecutive natural numbers is divisible by 6 (True/false).