find the remainder when the product of any three consecutive integers is divided by 6.

Asked by Amyra B | 17th Apr, 2013, 06:48: PM

Expert Answer:

Product of any 3 consecutive integers is divisible by 6, so the remainder on division by 6 would be 0. 
 
Proof:  Lets take three consecutive integers as n , n+1 and n+2. Now, there are 2 possibilities - 

1. Two numbers are odd and one is even. 

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

So the even number (irrespective of the fact that there would be 1 or 2 even numbers) is always divisible by two. And one of the odd numbers is divisible by three (remember you are taking three consecutive numbers and every third integer is a number series is divisible by 3). Therefore the product is divisible by two as well as three which means it is divisible by 2 X 3 =6.

Answered by  | 17th Apr, 2013, 08:52: PM

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