This week’s practice question looks deceivingly simple– try it out to test yourself before we post the answer tomorrow. Good luck!

2600 has how many positive divisors?

- 6
- 12
- 18
- 24
- 48

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

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By Margarette Jung on October 3, 2011 in Integer Properties, Math Concepts, Math Multiple Choice, Practice Question of the Week

This week’s practice question looks deceivingly simple– try it out to test yourself before we post the answer tomorrow. Good luck!

2600 has how many positive divisors?

- 6
- 12
- 18
- 24
- 48

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There are 24 divisors; these are,

1, 1 x 5, 1 x 13, 1 x 25, 1 x 5 x 13, 1 x 13 x 25,

(2^1), (2^1)x 5, (2^1)x 13, (2^1)x 25, (2^1)x 5 x 13, (2^1)x 13 x 25,

(2^2), (2^2)x 5, (2^2)x 13, (2^2)x 25, (2^2)x 5 x 13, (2^2)x 13 x 25,

(2^3), (2^3)x 5, (2^3)x 13, (2^3)x 25, (2^3)x 5 x 13, (2^3)x 13 x 25.

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Method:

2600 = 2^3 x 5^2 x 13

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Rule of thumb: Number of divisors = Product of (1 more than exponent of prime factors).

.

Interesting question:

What is the smallest number with 20 divisors? I think it’s 192. Do you agree?

.

MN

Hi, MN

Your answer to the practice question is correct! As for your question, 192 has 14 positive divisors (2^6 * 3), and the smallest number with 20 divisors is 240, since its prime factorization is 2^4 * 3 * 5.

Best,

Margarette

Thank you, Margarette.

.

And yes, it’s 240 – I was wrong earlier. Thanks again.

answer is D , 24……. 2600 = 2^3*5^2*13^1

so divisors turned out to be 4*3*2=24

answer is 24

2600 = 2^3 * 5^2 * 13

total positive divisors = (3+1)*(2+1)*(1+1)

= 24

the ans is D

the answer is 6