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Factors---Help!

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by vinay1983 » Tue Sep 24, 2013 5:10 pm
I have this problem with factors of numbers.

For example 12, has 3 and 4 as its factors according to me. But I have seen factors of 12 mentioned as 1, 3, 4, 12. Explain.

If "n" is a number, then are 1 and n factors of n?

If "2n" is a number, then are 1, n, 2 and 2n factors of 2n?

Is there any generalization in this?

I get most of questions on the above concept wrong :(
You can, for example never foretell what any one man will do, but you can say with precision what an average number will be up to!
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Source: — Problem Solving |

by [email protected] » Tue Sep 24, 2013 6:20 pm
Hi vinay1983,

I'll answer your questions first:

By definition, a "factor" is any number that divides EVENLY into a larger number. The GMAT tends to focus on positive factors only.

So, the factors of 12 are 1, 12, 2, 6, 3 and 4

By extension, if "n" is an integer, then both 1 and n are factors of n

**As an aside, 1 is a factor of EVERY integer.**

Working forward, if 2n is an integer then we still need to know a bit more about n. Is n an integer or not?

If n = 1/2, then 2n = 1 and the only factor of 1 is 1
If n = 3, then 2n = 6 and the factors are 1, 6, 2 and 3

In questions that ask about factors (or multiples) and involve variables, you'll find that TESTing values is an easy way to figure out the possibilities.

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by ganeshrkamath » Tue Sep 24, 2013 8:44 pm
vinay1983 wrote:I have this problem with factors of numbers.

For example 12, has 3 and 4 as its factors according to me. But I have seen factors of 12 mentioned as 1, 3, 4, 12. Explain.

If "n" is a number, then are 1 and n factors of n?

If "2n" is a number, then are 1, n, 2 and 2n factors of 2n?

Is there any generalization in this?

I get most of questions on the above concept wrong :(
Factor of a number is defined as any positive integer that wholly divides the given number.
According to this definition, 1 and the number itself are valid factors.

Example,
12 has the factors : 1,2,3,4,6,12
24 has the factors : 1,2,3,4,6,12,24

Rule 1: All factors of n are also factors of 2n.
Rule 2: The second highest factor of n is always <= n/2

Hope this helps.

Cheers
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Kelley School of Business (Class of 2016)
GMAT Score: 750 V40 Q51 AWA 5 IR 8
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