Q: What is the total or count of factors of the number 31,132,236?

 A: 72

How do I find the total factors of the number 31,132,236?

Step 1

Find the prime factorization of the number 31,132,236.

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

Factor Tree
31,132,236
Factor Arrows
215,566,118
Factor Arrows
27,783,059
Factor Arrows
32,594,353
Factor Arrows
17152,609
Factor Arrows
178,977
Factor Arrows
47191

The prime factorization in exponential form is: 22 x 31 x 172 x 471 x 1911

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.

31,132,236 = 22 x 31 x 172 x 471 x 1911
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)(d + 1)(e + 1)
Down Arrow
d(31132236) = (2 + 1)(1 + 1)(2 + 1)(1 + 1)(1 + 1)
Down Arrow
d(31132236) = (3)(2)(3)(2)(2)
Down Arrow
d(31132236) = 72

More numbers for you to try

Take a look at the factors page to see the factors of 31,132,236 and how to find them.

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