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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

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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, even

odd, 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 combination

For 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 combination

For 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
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