Factors---Help!

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vinay1983: Legendary Member; Posts: 643; Joined: Wed Aug 14, 2013 4:27 amFollowed by: 7 members; Thanked: 48 times

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!

Source: Beat The GMAT — Problem Solving | Tue Sep 24, 2013 5:10 pm

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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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Rich

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ganeshrkamath: Master | Next Rank: 500 Posts; Posts: 283; Joined: Sun Jun 23, 2013 11:56 pmFollowed by: 26 members; Location: Bangalore, India; Thanked: 97 times; GMAT Score:750

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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