How many distinct integers are factors of 90? : GMAT Problem Solving (PS)
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# How many distinct integers are factors of 90?

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

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

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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.
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Kudos [?]: 734 [0], given: 325

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

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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 .
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Kudos [?]: 9 [0], given: 11

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

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27 Jul 2015, 02:41
Just want to clear a concept that the formula to compute the no of factors of a number includes identical factors?

2^ 1 ∗3^ 2 ∗5^ 1 =90

therefore, for perfect square, we need to eliminate the identical factors?

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

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27 Jul 2015, 03:07
katzzzz wrote:
Just want to clear a concept that the formula to compute the no of factors of a number includes identical factors?

2^ 1 ∗3^ 2 ∗5^ 1 =90

therefore, for perfect square, we need to eliminate the identical factors?

The number of factors that you get is only the distinct factors and does not count the identical factors in case of perfect square twice..
eg 36=2^2*3^2..
no of factors= 3*3=9..
they are 1,2,3,4,6,9,12,18,36..
hope it clears the doubt
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Re: How many distinct integers are factors of 90? [#permalink]

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27 Jul 2015, 03:40
katzzzz wrote:
Just want to clear a concept that the formula to compute the no of factors of a number includes identical factors?

2^ 1 ∗3^ 2 ∗5^ 1 =90

therefore, for perfect square, we need to eliminate the identical factors?

Please refer two distinct concepts to calculate factors of any Number

1) By writing the Number as product of two Integers

2) By prime factorization and multiplying the powers of Distinct prime after adding one in each power of Primes
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Re: How many distinct integers are factors of 90? [#permalink]

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27 Jul 2015, 03:57
katzzzz wrote:
Just want to clear a concept that the formula to compute the no of factors of a number includes identical factors?

2^ 1 ∗3^ 2 ∗5^ 1 =90

therefore, for perfect square, we need to eliminate the identical factors?

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Joined: 16 May 2015
Posts: 46
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Kudos [?]: 9 [0], given: 11

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

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27 Jul 2015, 07:22
Hi Chetan and GMAR Insight,
thanks. clear now.

Hi Bunnel,
I will search the topic first for my future posts. thanks.
How many distinct integers are factors of 90?   [#permalink] 27 Jul 2015, 07:22
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