Q: What is the total or count of factors of the number 513,452,120?

 A: 32

How do I find the total factors of the number 513,452,120?

Step 1

Find the prime factorization of the number 513,452,120.

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

Factor Tree
513,452,120
Factor Arrows
2256,726,060
Factor Arrows
2128,363,030
Factor Arrows
264,181,515
Factor Arrows
512,836,303
Factor Arrows
71180,793

The prime factorization in exponential form is: 23 x 51 x 711 x 180,7931

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.

513,452,120 = 23 x 51 x 711 x 180,7931
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)(d + 1)
Down Arrow
d(513452120) = (3 + 1)(1 + 1)(1 + 1)(1 + 1)
Down Arrow
d(513452120) = (4)(2)(2)(2)
Down Arrow
d(513452120) = 32

More numbers for you to try

Take a look at the factors page to see the factors of 513,452,120 and how to find them.

Try the factor calculator.

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