Factor / Multiple Questions

[email protected] wrote:Anyone have suggestions for practicing / tackling these? These questions seem to be one of my weaker points...

Thanks in advance,

Eric

hi -

one thing that just about ALL factor / multiple problems on the gmat have in common is that they deal with PRIME FACTORIZATIONS.

therefore, if you see any problem about factors, multiples, and the like, you should try your best to recast the problem in terms of primes and prime factorizations, even if the original problem statement doesn't mention primes at all.

there is a staggering variety of factor/multiple problems out there, so it's difficult for me to give much more specific advice without seeing particular problems. nevertheless:
* if x is divisible by y, then ALL the prime factors of y, including the ones that appear more than once (if there are any), are also factors of x.
* if x is a factor of y, or y is a multiple of x, that's the same as 'x is divisible by y'.

this is only a start; if you have more specific questions, feel free to post them.

good luck.

[email protected] wrote:Does this ALWAYS hold true?

yes, always true. this is one of the great powers of prime factorizations.

in fact, the remaining primes are the # by which you would multiply the smaller number to get the larger number.

so, for instance, if
x = 2.2.2.3.3.3.5.5.7
and
y = 2.2.2.3.3.5.7
(where the dots represent multiplication),
then x is a multiple of y; in fact, since there's an "extra" 3 and 5 in the prime factorization of x, we know that x is 3.5 = 15 times y.