Q: What is the total or count of factors of the number 172,160?

 A: 32

How do I find the total factors of the number 172,160?

Step 1

Find the prime factorization of the number 172,160.

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

Factor Tree
172,160
Factor Arrows
286,080
Factor Arrows
243,040
Factor Arrows
221,520
Factor Arrows
210,760
Factor Arrows
25,380
Factor Arrows
22,690
Factor Arrows
21,345
Factor Arrows
5269

The prime factorization in exponential form is: 27 x 51 x 2691

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.

172,160 = 27 x 51 x 2691
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)
Down Arrow
d(172160) = (7 + 1)(1 + 1)(1 + 1)
Down Arrow
d(172160) = (8)(2)(2)
Down Arrow
d(172160) = 32

More numbers for you to try

Take a look at the factors page to see the factors of 172,160 and how to find them.

Try the factor calculator.

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