Q: What is the total or count of factors of the number 311,112?

 A: 48

How do I find the total factors of the number 311,112?

Step 1

Find the prime factorization of the number 311,112.

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

Factor Tree
311,112
Factor Arrows
2155,556
Factor Arrows
277,778
Factor Arrows
238,889
Factor Arrows
312,963
Factor Arrows
34,321
Factor Arrows
29149

The prime factorization in exponential form is: 23 x 32 x 291 x 1491

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.

311,112 = 23 x 32 x 291 x 1491
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)(d + 1)
Down Arrow
d(311112) = (3 + 1)(2 + 1)(1 + 1)(1 + 1)
Down Arrow
d(311112) = (4)(3)(2)(2)
Down Arrow
d(311112) = 48

More numbers for you to try

Take a look at the factors page to see the factors of 311,112 and how to find them.

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