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2600 has how many positive divisors?

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2600 has how many positive divisors? [#permalink] New post 29 Oct 2017, 01:33
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62% (00:29) correct 37% (00:15) wrong based on 8 sessions
2600 has how many positive divisors?

A. 6
B. 12
C. 18
D. 24
E. 48

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Re: 2600 has how many positive divisors? [#permalink] New post 29 Oct 2017, 04:03
2600 = 2^3 x 5^2 x 13

Number of positive divisors = (3+1)(2+1)(1+1) = 24
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Re: 2600 has how many positive divisors? [#permalink] New post 05 Jan 2018, 10:25
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Expert's post
Bunuel wrote:
2600 has how many positive divisors?

A. 6
B. 12
C. 18
D. 24
E. 48


To determine the number of positive divisors, we break 2,600 into primes, add 1 to the exponent of each unique prime, and then multiply those values together.

We see that 2,600 = 26 x 100 = 2 x 13 x 4 x 25 = 2^3 x 5^2 x 13^1.

Now we add 1 to each exponent and multiply those results:

(3 + 1)(2 + 1)(1 +1) = 24

Thus, 2,600 has 24 positive divisors.

Answer: D
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Re: 2600 has how many positive divisors?   [#permalink] 05 Jan 2018, 10:25
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