Q: What is the total or count of factors of the number 90,972?

 A: 54

How do I find the total factors of the number 90,972?

Step 1

Find the prime factorization of the number 90,972.

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

Factor Tree
90,972
Factor Arrows
245,486
Factor Arrows
222,743
Factor Arrows
37,581
Factor Arrows
32,527
Factor Arrows
7361
Factor Arrows
1919

The prime factorization in exponential form is: 22 x 32 x 71 x 192

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.

90,972 = 22 x 32 x 71 x 192
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)(d + 1)
Down Arrow
d(90972) = (2 + 1)(2 + 1)(1 + 1)(2 + 1)
Down Arrow
d(90972) = (3)(3)(2)(3)
Down Arrow
d(90972) = 54

More numbers for you to try

Take a look at the factors page to see the factors of 90,972 and how to find them.

Try the factor calculator.

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