" The product of three consecutive positive integers is divisible by "

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

Prove that one of every three consecutive positive integers is divisible by 3.

Prove that one of every three consecutive positive integers is divisible by 3.

Consider the following statements: 1. The product of any three consecutive integers is divisible by 6. 2. Any integer can be expressed in one of the three forms 3k,3k+1,3k+2 where k is an integer Which of the above statements is/are correct

Prove that the product of 2n consecutive negative integers is divisible by (2n)!

When product of r consecutive positive integers is divided by r! then the quotient is:

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.

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