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

Best Answer

Explanation:

Let us take the three consecutive positive integers as : a,a + 1,a + 2

A number when divided by 3, will have a remainder = 0 or 1 or 2

We can clearly see the numbers a,a + 1,a + 2 are always divisible by 3.

Similarly, we can show that when a number is divisible by 2, we get the remainder as 0 or 1

Clearly, 2m and 2(m+1) both are divisible by 2.

We can clearly see the numbers a,a + 1,a + 2 are always divisible by 2.

We can say that a,a + 1,a + 2 is always divisible by 2 ,3 ,6

Example: 

Let us take: 3,4,5 

3 x 4 x 5 = 60 

We can see that 60 is divisible by 6