Q: What is the total or count of factors of the number 86,520?

 A: 64

How do I find the total factors of the number 86,520?

Step 1

Find the prime factorization of the number 86,520.

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

Factor Tree
86,520
Factor Arrows
243,260
Factor Arrows
221,630
Factor Arrows
210,815
Factor Arrows
33,605
Factor Arrows
5721
Factor Arrows
7103

The prime factorization in exponential form is: 23 x 31 x 51 x 71 x 1031

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)(e + 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.

86,520 = 23 x 31 x 51 x 71 x 1031
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)(d + 1)(e + 1)
Down Arrow
d(86520) = (3 + 1)(1 + 1)(1 + 1)(1 + 1)(1 + 1)
Down Arrow
d(86520) = (4)(2)(2)(2)(2)
Down Arrow
d(86520) = 64

More numbers for you to try

Take a look at the factors page to see the factors of 86,520 and how to find them.

Try the factor calculator.

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