Q: What is the total or count of factors of the number 89,520?

 A: 40

How do I find the total factors of the number 89,520?

Step 1

Find the prime factorization of the number 89,520.

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

Factor Tree
89,520
Factor Arrows
244,760
Factor Arrows
222,380
Factor Arrows
211,190
Factor Arrows
25,595
Factor Arrows
31,865
Factor Arrows
5373

The prime factorization in exponential form is: 24 x 31 x 51 x 3731

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.

89,520 = 24 x 31 x 51 x 3731
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)(d + 1)
Down Arrow
d(89520) = (4 + 1)(1 + 1)(1 + 1)(1 + 1)
Down Arrow
d(89520) = (5)(2)(2)(2)
Down Arrow
d(89520) = 40

More numbers for you to try

Take a look at the factors page to see the factors of 89,520 and how to find them.

Try the factor calculator.

Explore more about the number 89,520:


Ask a Question