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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.
.
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.

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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.

.

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