Find How Many Factors Are in a Number


Finding how many factors are in a number is as easy a 1 2 3 if you know how to do it. But for larger numbers, you can't just count one by one. This is a nice trick to find how many factors are in an integer.

Steps

  1. 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.
  2. 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 23*32.
  3. Take all the exponents and add one to each of them.
    • In the example 23 and 32, the exponents are 3 and 2 - adding one to each will make them 4 and 3.
  4. 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.

Examples

7540

    • Prime Factorization - 225(29)(13). Now, because x1 = x, 29, 13, and 5 all have exponents to the first power.
    • Add exponents by one. 3, 2, 2, 2.
    • Multiply the modified exponents together. There are 24 factors of the number 7540.

15802

    • Prime Factorization - 2(7901)
    • Modify exponents - 2, 2
    • Multiply. There are four factors of the number 15802 - 1, 2, 7901, 15802. 7901 is a prime number.

Tips

  • The reason you add one to each exponent is the possibility of a number to the zeroth power. This means that, for the number 23, there are four combinations for the exponent which can be multiplied by another number: 20, 21, 22, and 23. You can multiply 20 by 72 which would still give you 72, as x0 = 1 (with the notable exception of 00, an indeterminate form)
  • This article is to tell you how many factors are in a number. This does not tell you how to Factor a Number.
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