Q: What is the total or count of factors of the number 120,380?

 A: 24

How do I find the total factors of the number 120,380?

Step 1

Find the prime factorization of the number 120,380.

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

Factor Tree
120,380
Factor Arrows
260,190
Factor Arrows
230,095
Factor Arrows
56,019
Factor Arrows
13463

The prime factorization in exponential form is: 22 x 51 x 131 x 4631

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.

120,380 = 22 x 51 x 131 x 4631
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)(d + 1)
Down Arrow
d(120380) = (2 + 1)(1 + 1)(1 + 1)(1 + 1)
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d(120380) = (3)(2)(2)(2)
Down Arrow
d(120380) = 24

More numbers for you to try

Take a look at the factors page to see the factors of 120,380 and how to find them.

Try the factor calculator.

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