Here’s this week’s practice question: there’s only one correct answer. We’ll be posting the answer tomorrow, good luck!

How many odd, positive divisors does 540 have?

A. 6

B. 8

C. 12

D. 15

E. 24

**Update**: Here’s the answer/explanation post!

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By Margarette Jung on November 14, 2011 in Integer Properties, Math Concepts, Math Multiple Choice, Math Question Types, Practice Question of the Week

Here’s this week’s practice question: there’s only one correct answer. We’ll be posting the answer tomorrow, good luck!

How many odd, positive divisors does 540 have?

A. 6

B. 8

C. 12

D. 15

E. 24

**Update**: Here’s the answer/explanation post!

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540 breaks down to 2^2 x 3^3 x 5. Since we’ve got only a handful, we can quickly list these out & count them – there are 8. Answer choice is “B”.

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However, if the resultant number was 3^24 x 5^19 – we simply can not count it out.

.

If we choose all possible numbers forming out of 3^3 x 5 we’ll get,

4 x 2 = 8

(there are 4 ways to choose from 3^3, we can choose either 3^0 or 3^1 or 3^2 or 3^3; and there are 2 ways to choose from 5; we can choose 5^0 or 5^1).

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For the hypothetical case, 3^24 x 5^19, we’ll get 25 x 20 = 500. [As indicated earlier, this simply can’t be counted by listing each of the 500 numbers in a GRE test].

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MN

i will go with 8

5^1 x 3^3=2×4=8

B

I’ll go with 8

odd divisors: 1, 3, 5, 9, 15, 27, 45, 135