Q: What is the total or count of factors of the number 108,800?

 A: 54

How do I find the total factors of the number 108,800?

Step 1

Find the prime factorization of the number 108,800.

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

Factor Tree
108,800
Factor Arrows
254,400
Factor Arrows
227,200
Factor Arrows
213,600
Factor Arrows
26,800
Factor Arrows
23,400
Factor Arrows
21,700
Factor Arrows
2850
Factor Arrows
2425
Factor Arrows
585
Factor Arrows
517

The prime factorization in exponential form is: 28 x 52 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)

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.

108,800 = 28 x 52 x 171
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)
Down Arrow
d(108800) = (8 + 1)(2 + 1)(1 + 1)
Down Arrow
d(108800) = (9)(3)(2)
Down Arrow
d(108800) = 54

More numbers for you to try

Take a look at the factors page to see the factors of 108,800 and how to find them.

Try the factor calculator.

Explore more about the number 108,800:


Ask a Question