# Real Numbers

by siddarth
(hyderabad,a.p,india)

"product of three consecutive numbers is divisible by 6" Is it true? then justify it.

### Comments for Real Numbers

 May 08, 2011 Multiply Consecutive Numbers by: Staff The question: by Siddarth (Hyderabad, a.p, India)"product of three consecutive numbers is divisible by 6" Is it true? then justify it.The answer: Yes, the product of three consecutive numbers is divisible by 6.There are only two possibilities for the even-odd combination of three consecutive numbers:even, odd, evenodd, even, odd For every three consecutive numbers, ONE OF THE NUMBERS IS ALWAYS DIVISIBLE BY 3. This number could be either an odd or an even number. Beyond this, there are two possibilities:(1) even, odd, even combinationFor every three consecutive numbers, at least one of the other numbers will be an even number, always divisible by 2. (Number divisible by 3)*(number divisible by 2)*(another number)Since this expression can always be divided by a 3, then divided again by 2, the entire expression can always be divided by a 6.(2) odd, even, odd combinationFor every three consecutive numbers, two of the numbers could be odd numbers which are not divisible by 3 or 2. However, since the remaining number is an even number, it can be divided by 3 and 2. (Number divisible by 3 and 2)*(another number)*(another number)Since this expression can always be divided by a 3, then divided again by 2, the entire expression can always be divided by a 6.Thanks for writing.Staff www.solving-math-problems.com

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