BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

Factors---Help!

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
User avatar
Legendary Member
Posts: 643
Joined: Wed Aug 14, 2013 4:27 am
Thanked: 48 times
Followed by:7 members

Factors---Help!

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!
Top
Source: — Problem Solving |

GMAT/MBA Expert

User avatar
Elite Legendary Member
Posts: 10392
Joined: Sun Jun 23, 2013 6:38 pm
Location: Palo Alto, CA
Thanked: 2867 times
Followed by:511 members
GMAT Score:800

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.

GMAT assassins aren't born, they're made,
Rich
Contact Rich at [email protected]
Image
Top
User avatar
Master | Next Rank: 500 Posts
Posts: 283
Joined: Sun Jun 23, 2013 11:56 pm
Location: Bangalore, India
Thanked: 97 times
Followed by:26 members
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
Every job is a self-portrait of the person who did it. Autograph your work with excellence.

Kelley School of Business (Class of 2016)
GMAT Score: 750 V40 Q51 AWA 5 IR 8
https://www.beatthegmat.com/first-attemp ... tml#688494
Top
Post new topic Post Reply
• Page 1 of 1