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

Redeem

Factor pair vs. prime factor

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Junior | Next Rank: 30 Posts
Posts: 23
Joined: Mon Mar 24, 2014 8:17 pm

Factor pair vs. prime factor

by aces021 » Wed May 13, 2015 11:20 am
How can I tell if a problem asks to find the factor pair or the prime factor?

ex: PS110: For the postive integers a,b, and k, a^k || b means that a^k is a divisor of b, but a^(k+1) is not a divisor of b. If k is a positive integer and 2^k || 72, then k is equal to....

vs.

ex: PS204: If n=4p where p is a prime number greater than 2 how many different positive even divisors does n have, including n?


The first one uses prime factorization to solve, the second one uses factor pairs to solve. Why? Why does "how many different positive even divisors" mean that you need to look at factor pairs and not just the prime factors?
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] » Thu May 14, 2015 9:26 am
Hi aces021,

Most Quant questions that you'll face can be solved in a variety of ways. Prime Factorization is a method for re-organizing math "data"; it's not an approach that you'll use too often on Test Day, but you're likely to come across a couple of questions in which you MIGHT use Prime Factorization to get to the solution. That doesn't necessarily mean that you *need* to use Prime Factorization though.

Questions from the OG often focus on just one approach to answering the question (although sometimes the writers will offer a second approach). If you don't "like" the solution that's offered, chances are pretty good that there is another way to go about solving the question. Many of those approaches have been discussed on this site.

To answer your immediate questions: any time a prompt discusses factors or division, then Prime Factorization might be an option (in most cases it won't be the "best" or fastest option though).

GMAT assassins aren't born, they're made,
Rich
Contact Rich at [email protected]
Image
Top
Junior | Next Rank: 30 Posts
Posts: 23
Joined: Mon Mar 24, 2014 8:17 pm

by aces021 » Fri May 15, 2015 7:53 am
[email protected] wrote:Hi aces021,

Most Quant questions that you'll face can be solved in a variety of ways. Prime Factorization is a method for re-organizing math "data"; it's not an approach that you'll use too often on Test Day, but you're likely to come across a couple of questions in which you MIGHT use Prime Factorization to get to the solution. That doesn't necessarily mean that you *need* to use Prime Factorization though.

Questions from the OG often focus on just one approach to answering the question (although sometimes the writers will offer a second approach). If you don't "like" the solution that's offered, chances are pretty good that there is another way to go about solving the question. Many of those approaches have been discussed on this site.

To answer your immediate questions: any time a prompt discusses factors or division, then Prime Factorization might be an option (in most cases it won't be the "best" or fastest option though).

GMAT assassins aren't born, they're made,
Rich

Thanks for your response. I ended up getting "PS204: If n=4p where p is a prime number greater than 2 how many different positive even divisors does n have, including n? " incorrect because I answered how many different positive prime factors there were NOT how many different positive factor pairs there were. I'm trying to figure out how the question alludes to factor pairs and not prime factors.
Top
User avatar
Legendary Member
Posts: 2663
Joined: Wed Jan 14, 2015 8:25 am
Location: Boston, MA
Thanked: 1153 times
Followed by:128 members
GMAT Score:770

by DavidG@VeritasPrep » Fri May 15, 2015 8:02 am
Thanks for your response. I ended up getting "PS204: If n=4p where p is a prime number greater than 2 how many different positive even divisors does n have, including n? " incorrect because I answered how many different positive prime factors there were NOT how many different positive factor pairs there were. I'm trying to figure out how the question alludes to factor pairs and not prime factors.
There's no reason to think about this question so abstractly. Rather than deliberating over whether they mean "factor pairs" or not, just pick an easy number and find those positive even divisors.

n = 4p. If p is greater than 2, let's say p =3. Now n = 4*3 = 12.
So let's list out the divisors of 12 and count the number of evens: 1, 2, 3, 4, 6, 12

There's four of them. And that's your answer.

(Incidentally, because we're asked how many even divisors there are, we can deduce that we're not simply being asked about prime bases.)
Veritas Prep | GMAT Instructor

Veritas Prep Reviews
Save $100 off any live Veritas Prep GMAT Course
Top
Post new topic Post Reply
• Page 1 of 1