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# How many distinct integers are factors of 90?

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Senior Manager
Joined: 10 Apr 2012
Posts: 280
Location: United States
Concentration: Technology, Other
GPA: 2.44
WE: Project Management (Telecommunications)
Followers: 3

Kudos [?]: 225 [0], given: 324

How many distinct integers are factors of 90? [#permalink]  11 Feb 2013, 00:26
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Difficulty:

15% (low)

Question Stats:

81% (01:15) correct 19% (00:30) wrong based on 52 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.
Math Expert
Joined: 02 Sep 2009
Posts: 26927
Followers: 4154

Kudos [?]: 39855 [1] , given: 5309

Re: How many distinct integers are factors of 90? [#permalink]  11 Feb 2013, 00:44
1
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: $$(1+1)(2+1)(1+1)=12$$.

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.
_________________
Senior Manager
Joined: 10 Apr 2012
Posts: 280
Location: United States
Concentration: Technology, Other
GPA: 2.44
WE: Project Management (Telecommunications)
Followers: 3

Kudos [?]: 225 [0], given: 324

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