Question

PROVE that the product of three
Consecutive positive integer is divsible
by 6​

Answer 1

Answer:

Step-by-step explanation:

Let the numbers be a, a+1,a+2

Product of these consecutive positive integers -

a(a+1)(a+2)

(a^2 + a)(a + 2)

a^3 + 3a^2 + 2a

According to divisibility rule of 6 -

2a is a multiple of 2, which means the product is divisible by 2; and

Sum of coefficients of the product, that is, 6 is a multiple of 3, which means it is also divisible by 3.

Since, the product is divisible by 2 and 3, so, it is divisible by 6