Q: What is the total or count of factors of the number 12,160?

 A: 32

How do I find the total factors of the number 12,160?

Step 1

Find the prime factorization of the number 12,160.

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

Factor Tree
12,160
Factor Arrows
26,080
Factor Arrows
23,040
Factor Arrows
21,520
Factor Arrows
2760
Factor Arrows
2380
Factor Arrows
2190
Factor Arrows
295
Factor Arrows
519

The prime factorization in exponential form is: 27 x 51 x 191

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.

12,160 = 27 x 51 x 191
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)
Down Arrow
d(12160) = (7 + 1)(1 + 1)(1 + 1)
Down Arrow
d(12160) = (8)(2)(2)
Down Arrow
d(12160) = 32

More numbers for you to try

Take a look at the factors page to see the factors of 12,160 and how to find them.

Try the factor calculator.

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