Question regarding divisibility- Pls. help

Question

Hi,
Could someone please confirm if the following statement is true?

If there is one EVEN integer in a series of consecutive integers, the product of the series is divisible by 2. If there are two even integers, the product of the series is divisible by 4.

I am a little confused since I thought somewhere I also read, if there are two consecutive even integers it is divisible by 8. I am not sure which one is correct! Please help.

Thanks

amitbharadwaj7 · Answer

Please note that any two consecutive even integers product will be divisible by 4 and 8 also. You may check by your self.

audiogal101 · Answer

what if the two integers are 0 and 2, is product divisible by 8?

Bunuel · Answer

0*2=0 --> 0 is divisible by 8.

Zero is divisible by EVERY integer except zero itself, since 0/integer=integer (or, which is the same, zero is a multiple of every integer).

KarishmaB · Answer

Don't bank on what you learn - it is easy to get confused in the test. Try to understand why this is so.

An even integer looks like this: 2a

Two even consecutive integers look like this: 2a, 4b
When you have two even consecutive integers, one of them must be divisible by 4 and the other will not be since a multiple of 4 comes in every fourth number e.g. (2, 4), (4, 6), (6, 8), (8, 10) etc

In a product has two consecutive even integers, it will have 2a*4b*.... i.e. it will have an 8. So it will be divisible by 8 (which automatically means it is divisible by 4 and 2 too)

Question regarding divisibility- Pls. help

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