How many distinct integers are factors of 90?

Oldest

Best Reply

Author

Message

TAGS:

Manager

Joined: 10 Apr 2012

Posts: 88

Followers: 0

Kudos [?]: 8 [0], given: 116

How many distinct integers are factors of 90? [#permalink]

11 Feb 2013, 01:26

00:00

Question Stats:

87% (01:12) correct

12% (00:42) wrong

based on 4 sessions

How many distinct integers are factors of 90?

A. 6
B. 8
C. 9
D. 10
E. 12

[Reveal] Spoiler:

Approach 2: Prime factorization:
21∗32∗51=90

Add 1 to each exponent and multiply them:
(1+1)(2+1)(1+1)=12

I did not follow the approach , why 're we adding 1 ? . I get confused with this type of problems . Where Can i find a clear explanation for this approach theoretically? Appreciate the help !

thanks

[Reveal] Spoiler: OA

Last edited by Bunuel on 11 Feb 2013, 01:41, edited 1 time in total.

Edited the question.

GMAT Club team member

Joined: 02 Sep 2009

Posts: 11534

Followers: 1795

Kudos [?]: 9566 [1] , given: 826

Re: How many distinct integers are factors of 90? [#permalink]

11 Feb 2013, 01:44

This post received
KUDOS

guerrero25 wrote:

How many distinct integers are factors of 90?

A. 6
B. 8
C. 9
D. 10
E. 12

[Reveal] Spoiler:

Approach 2: Prime factorization:
21∗32∗51=90

Add 1 to each exponent and multiply them:
(1+1)(2+1)(1+1)=12

I did not follow the approach , why 're we adding 1 ? . I get confused with this type of problems . Where Can i find a clear explanation for this approach theoretically? Appreciate the help !

thanks

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.

Back to the original question:

How many distinct integers are factors of 90?

A. 6
B. 8
C. 9
D. 10
E. 12

90=2*3^2*5, which means that the number of factors of 90 is: (1+1)(2+1)(1+1)=12.

Answer: E.

Similar 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

Hope it helps.
_________________

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

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. NEW!!!

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. NEW!!!

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

Find out what's new at GMAT Club - latest features and updates

Manager

Joined: 10 Apr 2012

Posts: 88

Followers: 0

Kudos [?]: 8 [0], given: 116

Re: How many distinct integers are factors of 90? [#permalink]

12 Feb 2013, 03:59

Hope it helps.[/quote]

Hi Bunuel,Thanks you so Much .. After going through the other posts you mentioned here , I could do any problem related to factors now .

Re: How many distinct integers are factors of 90? [#permalink] 12 Feb 2013, 03:59

		Similar topics	Author	Replies	Last post
Similar Topics:		How many total number of distinct positive factors are there	kpadma	13	28 Feb 2004, 20:07
		How many distinct prime factors do 4! and 8! have in common?	Macedon	2	27 Sep 2005, 04:13
		How many numbers can be a FACTOR of 90	Riuscita	7	04 Apr 2006, 22:21
	1	How many different positive integers are factors of 441?	lumone	4	02 Mar 2008, 14:01
		How many distinct positive factors does 30,030 have?	Drik	1	18 Dec 2012, 04:07

How many distinct integers are factors of 90?

Main navigation

GMAT Resources

Partners

MBA Resources

GMAT ® is a registered trademark of the Graduate Management Admission Council ® (GMAC ®). GMAT Club's website has not been reviewed or endorsed by GMAC.

GMAT Courses

Admissions Consulting

How many distinct integers are factors of 90?

How many distinct integers are factors of 90?

Main navigation

GMAT Resources

Partners

MBA Resources