Q: What is the total or count of factors of the number 30,564,632?

 A: 48

How do I find the total factors of the number 30,564,632?

Step 1

Find the prime factorization of the number 30,564,632.

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

Factor Tree
30,564,632
Factor Arrows
215,282,316
Factor Arrows
27,641,158
Factor Arrows
23,820,579
Factor Arrows
7545,797
Factor Arrows
777,971
Factor Arrows
103757

The prime factorization in exponential form is: 23 x 72 x 1031 x 7571

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.

30,564,632 = 23 x 72 x 1031 x 7571
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)(d + 1)
Down Arrow
d(30564632) = (3 + 1)(2 + 1)(1 + 1)(1 + 1)
Down Arrow
d(30564632) = (4)(3)(2)(2)
Down Arrow
d(30564632) = 48

More numbers for you to try

Take a look at the factors page to see the factors of 30,564,632 and how to find them.

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