Q: What is the total or count of factors of the number 311,203,224?

 A: 96

How do I find the total factors of the number 311,203,224?

Step 1

Find the prime factorization of the number 311,203,224.

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

Factor Tree
311,203,224
Factor Arrows
2155,601,612
Factor Arrows
277,800,806
Factor Arrows
238,900,403
Factor Arrows
312,966,801
Factor Arrows
34,322,267
Factor Arrows
17254,251
Factor Arrows
713,581

The prime factorization in exponential form is: 23 x 32 x 171 x 711 x 3,5811

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.

311,203,224 = 23 x 32 x 171 x 711 x 3,5811
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)(d + 1)(e + 1)
Down Arrow
d(311203224) = (3 + 1)(2 + 1)(1 + 1)(1 + 1)(1 + 1)
Down Arrow
d(311203224) = (4)(3)(2)(2)(2)
Down Arrow
d(311203224) = 96

More numbers for you to try

Take a look at the factors page to see the factors of 311,203,224 and how to find them.

Try the factor calculator.

Explore more about the number 311,203,224:


Ask a Question