Q: What is the total or count of factors of the number 108,468?

 A: 36

How do I find the total factors of the number 108,468?

Step 1

Find the prime factorization of the number 108,468.

Use a factor tree to assist with solving. Take a look at our prime factorization page for additional help.

Factor Tree
108,468
Factor Arrows
254,234
Factor Arrows
227,117
Factor Arrows
39,039
Factor Arrows
33,013
Factor Arrows
23131

The prime factorization in exponential form is: 22 x 32 x 231 x 1311

Step 2

Setup the equation for determining the number of factors or divisors. The equation is:

d(n) = (a + 1)(b + 1)(c + 1)(d + 1)

Where d(n) is equal to the number of divisors of the number and a, b, etc. are equal to the exponents of the prime factorization.

Now substitute the letters in the equation with the the exponents of your prime factorization and then solve to calculate the total number of divisors.

108,468 = 22 x 32 x 231 x 1311
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)(d + 1)
Down Arrow
d(108468) = (2 + 1)(2 + 1)(1 + 1)(1 + 1)
Down Arrow
d(108468) = (3)(3)(2)(2)
Down Arrow
d(108468) = 36

More numbers for you to try

Take a look at the factors page to see the factors of 108,468 and how to find them.

Try the factor calculator.

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