Problem Solving

2,600 has how many positive divisors?

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

The OA is D.

How can I calculate the total of divisors? Is there any formula? Experts, may you help me?

VJesus12 wrote:2,600 has how many positive divisors?

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

The OA is D.

How can I calculate the total of divisors? Is there any formula? Experts, may you help me?

Neat shortcut for finding the number of divisors of a given value.

First, take the prime factorization of the number in question: 2600 = 26 * 100 = 2 * 13 * 2^2 * 5^2 = 2^3 * 5^2 * 13

Next, add one to the exponent of each prime base and multiply the results. (Note that 13 is the same as 13^1): (3+1)(2+1)(1+1) = (4)(3)(2) = 24. The answer is D

2,600 has how many positive divisors?

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

The OA is D.

How can I calculate the total of divisors? Is there any formula? Experts, may you help me?

Hi VJesus12,
Let's take a look at your question.

We are asked to find the number of positive divisors of 2600.
In order to find number of positive divisors a number has, we find the prime factorization, and add one to all the exponents and multiply them.

Let's write 2600 as a product of its prime factors.
$$2600=\ 26\ \times100$$
$$2600=\ 2\times13\ \times10\times10$$
$$2600=\ 2\times13\ \times2\times5\times2\times5$$

2600 is now written as a product of its prime factors.
Let's now write the factors using exponents.
$$2600=\ 2^3\times5^2\times13^1$$

To find the number of positive divisors of 2600, add 1 to each exponent and multiply them.
$$=\left(3+1\right)\left(2+1\right)\left(1+1\right)$$
$$=\left(4\right)\left(3\right)\left(2\right)$$
$$=24$$

Therefore, Option D is correct.

Hope it helps.
I am available if you'd like any follow up.

If it's easier to see this visually, check out this great tutorial.

In the future, remember that Google is your friend! In a pinch you can usually find walkthroughs of most basic formulas such as this without having to wait a few hours for an expert to reply.