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

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CR Forum Moderator
Status: The best is yet to come.....
Joined: 10 Mar 2013
Posts: 499

Kudos [?]: 218 [0], given: 197

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

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20 Oct 2017, 06:10
00:00

Difficulty:

15% (low)

Question Stats:

68% (00:19) correct 32% (00:15) wrong based on 28 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

Kudos [?]: 218 [0], given: 197

Board of Directors
Status: Aiming MBA
Joined: 18 Jul 2015
Posts: 2857

Kudos [?]: 963 [1], given: 69

Location: India
Concentration: Healthcare, Technology
GPA: 3.65
WE: Information Technology (Health Care)
How many factors of 2^3*3^4*5^5 are odd numbers? [#permalink]

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20 Oct 2017, 06:16
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 I improved from V21 to V40! ?

Kudos [?]: 963 [1], given: 69

How many factors of 2^3*3^4*5^5 are odd numbers?   [#permalink] 20 Oct 2017, 06:16
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