Question

prove that the product of three consecutive positive integer is divisible by 6​

Answer 1

Step-by-step explanation:

Prove that the product of three consecutive positive integers is divisible by 6. ... so, we can say that one of the numbers n, n + 1 and n + 2 is always divisible by 3. n (n + 1) (n + 2) is divisible by 3. similarly, when a no. is divisible by 2, remainders obtained is 0 or 1.

Answer 2

Step-by-step explanation:

Let n be any positive integer is of the form 6q or, 6q+1 or, 6q+2 or, 6q+3 or, 6q+4 or, 6q+5.

If n=6q, then

n(n+1)(n+2)=6q(6q+1)(6q+2), which is divisible by 6

If n=6q+1, then

n(n+1)(n+2)=(6q+1)(6q+2)(6q+3)=6(6q+1)(3q+1)(2q+1),

which is divisible by 6.

If n=6q+2, then

n(n+1)(n+2)=(6q+2)(6q+3)(6q+4)=12(3q+1)(2q+1)(2q+3),

which is divisible by 6.

Similarly , n(n+1)(n+2) is divisible by 6 if n=6q+3 or, 6q+4 or, 6q+5.