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Re: Divisors VS Factors [#permalink]
14 Apr 2009, 13:58

Nach0 wrote:

What's the difference between divisors and factors?

It seems like DIVISORS of X include 1 and X, but FACTORS don't.

Am I right?

It would help with questions like, "How many factors of Y are there?" or "Does Z have three positive factors?"

When discussing numbers, the words 'divisor' and 'factor' have the same meaning. '1' is a factor and a divisor of every positive integer. _________________

Nov 2011: After years of development, I am now making my advanced Quant books and high-level problem sets available for sale. Contact me at ianstewartgmat at gmail.com for details.

Re: Divisors VS Factors [#permalink]
17 Apr 2009, 08:13

lgon wrote:

Please correct me if I am wrong.

Divisor can/cannot completely divide the number. But a factor will always divide it completely.

No, that's not correct. Divisors must completely divide the number for which they are a divisor. Three is a divisor of six, for example, but not of seven. There wouldn't be much reason to have the term 'divisor' if divisors didn't need to divide completely; if that were true, then every positive integer would be a divisor of every other positive integer. _________________

Nov 2011: After years of development, I am now making my advanced Quant books and high-level problem sets available for sale. Contact me at ianstewartgmat at gmail.com for details.

Re: Divisors VS Factors [#permalink]
21 Apr 2009, 15:25

Other responders have covered the main point: the words "divisor" and "factor" are completely interchangeable.

For example, the divisors of 12 are 1, 2, 3, 4, 6, and 12. The factors of 12 are... you guessed it. The exact same list.

Thus, you can make the observation that 1 is a factor/divisor of every number, and every number is a factor/divisor of itself.

Make sure not to confuse divisors with multiples! Multiples of 12 include 12, 24, 36, etc. That's right, every number is considered a multiple of itself.

Also, note the following list of facts:

The factors of 12 are 1, 2, 3, 4, 6, and 12. The prime factorization of 12 is 12= 2*2*3. 12 has 6 factors (listed above). The unique prime factors of 12 are only 2 and 3.

Hope this helps keep all of those things distinct!

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