Q: What is the total or count of factors of the number 313,485,656?

 A: 32

How do I find the total factors of the number 313,485,656?

Step 1

Find the prime factorization of the number 313,485,656.

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

Factor Tree
313,485,656
Factor Arrows
2156,742,828
Factor Arrows
278,371,414
Factor Arrows
239,185,707
Factor Arrows
113,562,337
Factor Arrows
23315,289

The prime factorization in exponential form is: 23 x 111 x 2331 x 15,2891

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.

313,485,656 = 23 x 111 x 2331 x 15,2891
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)(d + 1)
Down Arrow
d(313485656) = (3 + 1)(1 + 1)(1 + 1)(1 + 1)
Down Arrow
d(313485656) = (4)(2)(2)(2)
Down Arrow
d(313485656) = 32

More numbers for you to try

Take a look at the factors page to see the factors of 313,485,656 and how to find them.

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