Find all School-related info fast with the new School-Specific MBA Forum

It is currently 21 Oct 2014, 02:31

Close

GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

Finding Number of Factors of an integer - question?

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
Intern
Intern
avatar
Joined: 25 Aug 2013
Posts: 4
Followers: 0

Kudos [?]: 0 [0], given: 15

Finding Number of Factors of an integer - question? [#permalink] New post 27 Nov 2013, 05:52
Hi,

Can anyone please help me with the formula for finding the total no. of factors of an integer?

The usual way is prime factorization; then increasing the exponent of each prime factor by one; and multiplying the raised numbers.

E.g:

Q. Find the no. of factors of 90?

A.

90 = 2^1 x 3^2 x 5^1

So total factors = (1+1) x (2+1) x (1+1) = 2 x 3 x 2 = 12.

I have a test prep where solution actually doubles this answer saying that 12 are positive factors and there are as many negative factors.

So the total no. of factors should be 12 x 2 = 24.

But I researched a bit on the internet and almost everywhere they don't double the answer, i.e. they say answer is 12.

What is right on GMAT?

Thanks,
federite
Kaplan GMAT Prep Discount CodesKnewton GMAT Discount CodesGMAT Pill GMAT Discount Codes
BSchool Forum Moderator
avatar
Status: busyness school student
Joined: 09 Sep 2013
Posts: 371
Location: United States
GMAT 1: 740 Q52 V38
Followers: 8

Kudos [?]: 206 [0], given: 129

Premium Member
Re: Finding Number of Factors of an integer - question? [#permalink] New post 27 Nov 2013, 06:05
You are correct - there are 12 factors in the number 90.

Generally, you do not include negative numbers. I'd be curious as to the actual wording of the question of the test prep.
_________________

My review of some of the CAT practice exams
You can usually find me on gmatclub's chat.

Intern
Intern
avatar
Joined: 25 Aug 2013
Posts: 4
Followers: 0

Kudos [?]: 0 [0], given: 15

Re: Finding Number of Factors of an integer - question? [#permalink] New post 27 Nov 2013, 06:13
Thanks for the reply.
The actual wording was what is the total number of factors of (a positive integer). I don't remember the exact number though.

Adding the negative number of factors sounds logical though.

Not sure whether I should do that. Fyi - The GMAT Club Math book doesn't add the negative factors. So doesn't MGMAT strategy guide.

Posted from my mobile device Image
1 KUDOS received
BSchool Forum Moderator
avatar
Status: busyness school student
Joined: 09 Sep 2013
Posts: 371
Location: United States
GMAT 1: 740 Q52 V38
Followers: 8

Kudos [?]: 206 [1] , given: 129

Premium Member
Re: Finding Number of Factors of an integer - question? [#permalink] New post 27 Nov 2013, 06:19
1
This post received
KUDOS
If it's just "find total number of factors of x", then do not include negative numbers. Factors should be positive, as prime numbers are. Factors are essentially prime factorization.
_________________

My review of some of the CAT practice exams
You can usually find me on gmatclub's chat.

Expert Post
2 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 23351
Followers: 3601

Kudos [?]: 28693 [2] , given: 2809

Re: Finding Number of Factors of an integer - question? [#permalink] New post 27 Nov 2013, 06:26
2
This post received
KUDOS
Expert's post
federite wrote:
Hi,

Can anyone please help me with the formula for finding the total no. of factors of an integer?

The usual way is prime factorization; then increasing the exponent of each prime factor by one; and multiplying the raised numbers.

E.g:

Q. Find the no. of factors of 90?

A.

90 = 2^1 x 3^2 x 5^1

So total factors = (1+1) x (2+1) x (1+1) = 2 x 3 x 2 = 12.

I have a test prep where solution actually doubles this answer saying that 12 are positive factors and there are as many negative factors.

So the total no. of factors should be 12 x 2 = 24.

But I researched a bit on the internet and almost everywhere they don't double the answer, i.e. they say answer is 12.

What is right on GMAT?

Thanks,
federite


Factor is a "positive divisor" (at least on the GMAT). So, for example the factors of 4 are 1, 2, and 4 ONLY.

Finding the Number of Factors of an Integer

First make prime factorization of an integer n=a^p*b^q*c^r, where a, b, and c are prime factors of n and p, q, and r are their powers.

The number of factors of n will be expressed by the formula (p+1)(q+1)(r+1). NOTE: this will include 1 and n itself.

Example: Finding the number of all factors of 450: 450=2^1*3^2*5^2

Total number of factors of 450 including 1 and 450 itself is (1+1)*(2+1)*(2+1)=2*3*3=18 factors.

For more check: math-number-theory-88376.html

Questions to practice:
how-many-odd-positive-divisors-does-540-have-106082.html
how-many-factors-does-36-2-have-126422.html
how-many-different-positive-integers-are-factor-of-130628.html
how-many-distinct-positive-factors-does-30-030-have-144326.html
m02-72467.html

Hope this helps.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
25 extra-hard Quant Tests

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Intern
Intern
avatar
Joined: 25 Nov 2013
Posts: 15
Location: Italy
GMAT 1: 720 Q49 V38
Followers: 0

Kudos [?]: 12 [0], given: 6

Re: Finding Number of Factors of an integer - question? [#permalink] New post 28 Nov 2013, 04:37
Definition from Manhattan GMAT, page 15 of Number Properties strategy guide:
"A factor is a positive integer that divides evenly into an integer". So, at least in the GMAT world, consider only positive factor.
Factor and divisor means the same thing, and from Wikipedia:
"Divisors can be negative as well as positive, although sometimes the term is restricted to positive divisors. For example, there are six divisors of 4; they are 1, 2, 4, −1, −2, and −4, but only the positive ones (1, 2, and 4) would usually be mentioned."
So in the Math world you should consider also negative ones. But this is not the case.
Re: Finding Number of Factors of an integer - question?   [#permalink] 28 Nov 2013, 04:37
    Similar topics Author Replies Last post
Similar
Topics:
Experts publish their posts in the topic question on number of factors Vips0000 3 07 Nov 2012, 02:59
Experts publish their posts in the topic How to find out the # of factors a particular number has? Liquidus 4 16 Jun 2011, 04:11
Number properties question - prime factors chloeholding 3 01 May 2011, 00:51
Experts publish their posts in the topic How can you find the number of factors of an integer, say parsifal 4 24 Dec 2007, 13:41
What is the number of positive integers that are factors of TeHCM 9 05 Dec 2005, 23:23
Display posts from previous: Sort by

Finding Number of Factors of an integer - question?

  Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Privacy Policy| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group and phpBB SEO

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.