Q: What is the total or count of factors of the number 84,513,121?

 A: 32

How do I find the total factors of the number 84,513,121?

Step 1

Find the prime factorization of the number 84,513,121.

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

Factor Tree
84,513,121
Factor Arrows
712,073,303
Factor Arrows
111,097,573
Factor Arrows
1957,767
Factor Arrows
61947

The prime factorization in exponential form is: 71 x 111 x 191 x 611 x 9471

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.

84,513,121 = 71 x 111 x 191 x 611 x 9471
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)(d + 1)(e + 1)
Down Arrow
d(84513121) = (1 + 1)(1 + 1)(1 + 1)(1 + 1)(1 + 1)
Down Arrow
d(84513121) = (2)(2)(2)(2)(2)
Down Arrow
d(84513121) = 32

More numbers for you to try

Take a look at the factors page to see the factors of 84,513,121 and how to find them.

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