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How to Determine the Number of Divisors in an Integer

A divisor, also called a factor, is a number that divides evenly into another number without leaving a remainder. Every number has at least two divisors, itself and 1. Some numbers, called prime numbers, have only those two divisors, but most numbers have at least one other divisor. (For example, every even number greater than 2 can be divided evenly by 2.) Divisors are easy to find by dividing your number by smaller numbers.

Things You'll Need

A calculator (optional)

Instructions

- 1
  Choose an example number. For instance, consider the number 24. As a given, the first two divisors are 1 and 24.
- 2
  Divide the number by smaller numbers. Because it's an even number, you can divide it by 2: 24 / 2 = 12. Because there is no remainder, 2 and 12 are divisors.
- 3
  Continue with 3 and 4: 24 / 3 = 8. So 3 and 8 are divisors. And 24 / 4 = 6. So 4 and 6 are divisors.
  
  If you try to divide 24 by 5, you'll get 4 with a remainder of 4. Because dividing by 5 leaves a remainder, 5 is not a divisor.
- 4
  Decide if you need to continue dividing. The next number is 6, but you already know that number is a divisor. So you can stop here.
- 5
  Count up the divisors: You identified 1, 2, 3, 4, 6, 8, 12 and 24 as divisors. So there are eight divisors in all.

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