Q: What is the total or count of factors of the number 9,072?

 A: 50

How do I find the total factors of the number 9,072?

Step 1

Find the prime factorization of the number 9,072.

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

Factor Tree
9,072
Factor Arrows
24,536
Factor Arrows
22,268
Factor Arrows
21,134
Factor Arrows
2567
Factor Arrows
3189
Factor Arrows
363
Factor Arrows
321
Factor Arrows
37

The prime factorization in exponential form is: 24 x 34 x 71

Step 2

Setup the equation for determining the number of factors or divisors. The equation is:

d(n) = (a + 1)(b + 1)(c + 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.

9,072 = 24 x 34 x 71
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)
Down Arrow
d(9072) = (4 + 1)(4 + 1)(1 + 1)
Down Arrow
d(9072) = (5)(5)(2)
Down Arrow
d(9072) = 50

More numbers for you to try

Take a look at the factors page to see the factors of 9,072 and how to find them.

Try the factor calculator.

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