Q: What is the total or count of factors of the number 310,708,288?

 A: 112

How do I find the total factors of the number 310,708,288?

Step 1

Find the prime factorization of the number 310,708,288.

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

Factor Tree
310,708,288
Factor Arrows
2155,354,144
Factor Arrows
277,677,072
Factor Arrows
238,838,536
Factor Arrows
219,419,268
Factor Arrows
29,709,634
Factor Arrows
24,854,817
Factor Arrows
11441,347
Factor Arrows
2319,189
Factor Arrows
31619

The prime factorization in exponential form is: 26 x 111 x 231 x 311 x 6191

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.

310,708,288 = 26 x 111 x 231 x 311 x 6191
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)(d + 1)(e + 1)
Down Arrow
d(310708288) = (6 + 1)(1 + 1)(1 + 1)(1 + 1)(1 + 1)
Down Arrow
d(310708288) = (7)(2)(2)(2)(2)
Down Arrow
d(310708288) = 112

More numbers for you to try

Take a look at the factors page to see the factors of 310,708,288 and how to find them.

Try the factor calculator.

Explore more about the number 310,708,288:


Ask a Question