How to Find How Many Factors Are in a Number

Identify the number. Any number in the world, but it's best to start with the simpler ones. Take 72, for example, but the number could be denoted by a variable.

Calculate the Prime Factorization of the number. There are many methods of doing this, but usually, the simplest way is to make a factor tree. This works because according to number theory, every integer (except -1, 0, and 1) has a number of prime numbers that, when multiplied together, will equal the number. Remember that 0 and 1 are not prime numbers. 72 should be factorized into 2 and 36, 2, 6, and 6, and finally, 2, 2, 3, 2, 3, which equals 2*3.

Take all the exponents and add one to each of them. In the example 2 and 3, the exponents are 3 and 2 - adding one to each will make them 4 and 3.

Multiply the modified exponents together. 4 x 3 = 12. There are 12 factors for the number 72 - 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, and 72.