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

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

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New post 20 Oct 2017, 07:10
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A
B
C
D
E

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  15% (low)

Question Stats:

73% (00:24) correct 28% (00:19) wrong based on 40 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

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

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New post 20 Oct 2017, 07:16
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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

Hence, answer must be B.
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How many factors of 2^3*3^4*5^5 are odd numbers? &nbs [#permalink] 20 Oct 2017, 07:16
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