How many odd, positive divisors does 540 have? GMAT Problem Solving

Question: How many odd, positive divisors does 540 have?

         A. 6
         B. 8
         C.12
         D. 15
         E. 24

Answer: B

Approach Solution (1):
Make a prime factorization of a number: 540=2² * 3³ * 5
And get rid of powers of 2 as they give even factors
You'll have 3³ * 5 which has (3 + 1)(1 + 1) = 8 factors
Correct option: B

Approach Solution (2):
So to find thetotal number of factors, we can add one to each to power in the prime factorization of an integer, then multiply all the (power + 1)s together. For 540, we would have (2 + 1)(3 + 1)(1 + 1) = 24 factors.
To find thenumber of odd factors(which includes 1), we can exclude any power of 2 and do the same. For 540, we have (3 + 1)(1 + 1) = 8 odd positive factors.
Correct option: B

Approach Solution (3):
1 * 540 = 540
2 * 270 = 540
3 * 180 = 540
4 * 135 = 540
5 * 108 = 540
6 * 90 = 540
9 * 60 = 540
10 * 54 = 540
12 * 45 = 540
15 * 36 = 540
18 * 30 = 540
20 * 27 = 540
So the odd divisors are 1, 3, 5, 9, 15, 27, 45, and 135
So the number of odd divisors is 8
Correct option: B

“How many odd, positive divisors does 540 have?”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book “GMAT Official Guide Quantitative Review”. To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. The GMAT Quant topic in the problem-solving part requires calculative mathematical problems that should be solved with proper mathematical knowledge.

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