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# How many factors of 2^3*3^4*5^5 are odd numbers?

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Retired Moderator
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Joined: 10 Mar 2013
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How many factors of 2^3*3^4*5^5 are odd numbers? [#permalink]

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20 Oct 2017, 07:10
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Difficulty:

25% (medium)

Question Stats:

69% (00:18) correct 31% (00:19) wrong based on 36 sessions

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How many factors of $$2^3*3^4*5^5$$ are odd numbers?

A. 20
B. 30
C. 90
D. 100
E. 120
[Reveal] Spoiler: OA

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Hasan Mahmud

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Joined: 18 Jul 2015
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How many factors of 2^3*3^4*5^5 are odd numbers? [#permalink]

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20 Oct 2017, 07:16
1
KUDOS
To find out the number of ODD factors, consider that there must not be any 2 in the product because 2 will make everything even.

That means find out the number of factors of $$2^0*3^4*5^5$$

As per the formula, $$a^p*b^q*c^r$$, we have number of factors = (p+1)(q+1)(r+1)

Therefore, for our question I can say, number of Odd factors = (0+1) ( 4+1)(5+1) = 5*6 = 30

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How many factors of 2^3*3^4*5^5 are odd numbers?   [#permalink] 20 Oct 2017, 07:16
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