Q: What is the total or count of factors of the number 28,560?

 A: 80

How do I find the total factors of the number 28,560?

Step 1

Find the prime factorization of the number 28,560.

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

Factor Tree
28,560
Factor Arrows
214,280
Factor Arrows
27,140
Factor Arrows
23,570
Factor Arrows
21,785
Factor Arrows
3595
Factor Arrows
5119
Factor Arrows
717

The prime factorization in exponential form is: 24 x 31 x 51 x 71 x 171

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.

28,560 = 24 x 31 x 51 x 71 x 171
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)(d + 1)(e + 1)
Down Arrow
d(28560) = (4 + 1)(1 + 1)(1 + 1)(1 + 1)(1 + 1)
Down Arrow
d(28560) = (5)(2)(2)(2)(2)
Down Arrow
d(28560) = 80

More numbers for you to try

Take a look at the factors page to see the factors of 28,560 and how to find them.

Try the factor calculator.

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