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.
.
Method:
2600 = 2^3 x 5^2 x 13
.
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

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.

Magoosh blog comment policy: To create the best experience for our readers, we will only approve comments that are relevant to the article, general enough to be helpful to other students, concise, and well-written! 😄 Due to the high volume of comments across all of our blogs, we cannot promise that all comments will receive responses from our instructors.

We highly encourage students to help each other out and respond to other students' comments if you can!

If you are a Premium Magoosh student and would like more personalized service from our instructors, you can use the Help tab on the Magoosh dashboard. Thanks!

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.

.

Method:

2600 = 2^3 x 5^2 x 13

.

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