Divisors VS Factors

Question

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?"

xunil56 · Answer

This is my first post, please correct if there is any inconsistency:

Let's look at something for this "divisor" and "factor"

If x & y are integers and x != 0 
then 
x is a factor (divisor) of y 
when y = xn (where n is some integer)

a little further
y/x is mean to be looked at as y is the dividend and x is a divisor

Hopefully this makes sense !

IanStewart · Answer

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

lgon · Answer

Please correct me if I am wrong.

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

IanStewart · Answer

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.

Liquidhypnotic · Answer

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!

mankhu8 · Answer

Thanks Intern for the crisp explanation, it will really help.

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

Divisors VS Factors

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards