Q: What is the total or count of factors of the number 313,243,424?

 A: 48

How do I find the total factors of the number 313,243,424?

Step 1

Find the prime factorization of the number 313,243,424.

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

Factor Tree
313,243,424
Factor Arrows
2156,621,712
Factor Arrows
278,310,856
Factor Arrows
239,155,428
Factor Arrows
219,577,714
Factor Arrows
29,788,857
Factor Arrows
13752,989
Factor Arrows
1939,631

The prime factorization in exponential form is: 25 x 131 x 191 x 39,6311

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.

313,243,424 = 25 x 131 x 191 x 39,6311
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)(d + 1)
Down Arrow
d(313243424) = (5 + 1)(1 + 1)(1 + 1)(1 + 1)
Down Arrow
d(313243424) = (6)(2)(2)(2)
Down Arrow
d(313243424) = 48

More numbers for you to try

Take a look at the factors page to see the factors of 313,243,424 and how to find them.

Try the factor calculator.

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