Q: What is the total or count of factors of the number 310,325,148?

 A: 96

How do I find the total factors of the number 310,325,148?

Step 1

Find the prime factorization of the number 310,325,148.

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

Factor Tree
310,325,148
Factor Arrows
2155,162,574
Factor Arrows
277,581,287
Factor Arrows
325,860,429
Factor Arrows
38,620,143
Factor Arrows
32,873,381
Factor Arrows
7410,483
Factor Arrows
601683

The prime factorization in exponential form is: 22 x 33 x 71 x 6011 x 6831

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)(e + 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.

310,325,148 = 22 x 33 x 71 x 6011 x 6831
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)(d + 1)(e + 1)
Down Arrow
d(310325148) = (2 + 1)(3 + 1)(1 + 1)(1 + 1)(1 + 1)
Down Arrow
d(310325148) = (3)(4)(2)(2)(2)
Down Arrow
d(310325148) = 96

More numbers for you to try

Take a look at the factors page to see the factors of 310,325,148 and how to find them.

Try the factor calculator.

Explore more about the number 310,325,148:


Ask a Question