prove that product of three consecutive numbers are divisible by 6.

Asked by prajjawal banati | 2nd Feb, 2014, 04:27: PM

Expert Answer:

This proof involves simple logic. 

When you are taking three numbers then only one of the following is possible: 

1. Two numbers are odd and one is even. 

2. Or two numbers are even and one is odd. 

So the even number is always divisible by two. And one of the odd numbers is divisible by three (remember you are taking three consecutive numbers). Therefore the product is divisible by two as well as three which means it is divisible by 2 X 3 =6. 

Answered by  | 3rd Apr, 2014, 10:23: AM

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