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# Around the World in 80 Questions (Day 5): What is the number of

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Re: Around the World in 80 Questions (Day 5): What is the number of [#permalink]
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Bunuel wrote:
What is the number of positive factors of 900 that are multiples of 5?

A. 27
B. 21
C. 18
D. 15
E. 9
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900 = 2^2 * 3^2 * 5^2
Possible factors are formed by a combination of individual factors of the primes:
For 2: 2^0, 2^1, 2^2
For 3: 3^0, 3^1, 3^2
For 5: 5^0, 5^1, 5^2

Since we need the factors that are multiple of 5, the possible options for 5 must be 5^1 and 5^2 only
Thus, total number of combinations = 3 * 3 * 2 = 18