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How many distinct integers are factors of 90?

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Senior Manager
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Joined: 10 Apr 2012
Posts: 265
Location: United States
Concentration: Technology, Other
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WE: Project Management (Telecommunications)
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Kudos [?]: 80 [0], given: 318

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How many distinct integers are factors of 90? [#permalink] New post 11 Feb 2013, 00:26
1
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A
B
C
D
E

Difficulty:

  5% (low)

Question Stats:

83% (01:15) correct 17% (00:30) wrong based on 41 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, 00:41, edited 1 time in total.
Edited the question.
Expert Post
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Kudos [?]: 22332 [1] , given: 2615

Re: How many distinct integers are factors of 90? [#permalink] New post 11 Feb 2013, 00:44
1
This post received
KUDOS
Expert's post
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:
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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.
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Senior Manager
Senior Manager
avatar
Joined: 10 Apr 2012
Posts: 265
Location: United States
Concentration: Technology, Other
GPA: 2.44
WE: Project Management (Telecommunications)
Followers: 2

Kudos [?]: 80 [0], given: 318

GMAT ToolKit User Premium Member CAT Tests
Re: How many distinct integers are factors of 90? [#permalink] New post 12 Feb 2013, 02:59
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, 02:59
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How many distinct integers are factors of 90?

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