Primes & Divisibility

[shanice]

Hi guys,

Can someone please help me with the below questions?

1)[u]Factor Foundation Rule (Manhattan Gmat)[/u]

[b]If a is a factor of b, and b is a factor of c, then a is a factor of c.[/b]
Meaning : Any integer is divisible by all of its factors and it is also divisible by all of the FACTORS of its factors.
Example : 72/12 = 6 (so, can I consider that a=12, b=72, c=6. Is my understanding correct?)

2) If x is an even integer, is x(x+1)(x+2) divisible by 4?
Answer is yes.


Thank you.

[Bill@VeritasPrep]

Your understanding is almost correct. In your example, it should be a=6, b=12, and c=72.

As for the question, to be divisible by 4, an integer must have two 2's as factors. Since x is even, (x+2) is also even, so x(x+1)(x+2) has two 2's and must be divisible by 4.

[Birottam Dutta]

As an addition to the above problem, you may also note the following:

x(X+1)(x+2) is always divisible by 24 if x is even.

Try and figure this out as well. The easiest way to do this is to assume values of x and try. Even without assuming the values, you can arrive at the answer.

Think about it!

[shanice]

Yes, you're right, Dutta. It worked.

Thank you Bill and Dutta.