How to Calculate Number of Divisors

Calculating the Number of Divisors

• 1

  Perform the prime factorization of the number. For example, if the given number was 60, you could break it into two times 30. Two is prime, but 30 is not, so you would further break it down to two times three times 10. Two and three are prime, but 10 is not, so you could further break it down into two times three times five times two. All four numbers are prime so you are finished with this step.

• 2

  Simplify the prime numbers into exponential form, if possible. For example, two times three times five times two would become two squared times three times five.

• 3

  Add one to each exponent. For example, two squared's exponent is two and when one is added it becomes three. Three's exponent is one so it becomes two. Five's exponent is one so it becomes two.

• 4

  Multiply the exponents. In this example, three times two times two. This gives you 12, which means there are 12 divisors of 60.