Q: What is the total or count of factors of the number 54,202,324?

 A: 48

How do I find the total factors of the number 54,202,324?

Step 1

Find the prime factorization of the number 54,202,324.

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

Factor Tree
54,202,324
Factor Arrows
227,101,162
Factor Arrows
213,550,581
Factor Arrows
111,231,871
Factor Arrows
1772,463
Factor Arrows
233311

The prime factorization in exponential form is: 22 x 111 x 171 x 2331 x 3111

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.

54,202,324 = 22 x 111 x 171 x 2331 x 3111
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)(d + 1)(e + 1)
Down Arrow
d(54202324) = (2 + 1)(1 + 1)(1 + 1)(1 + 1)(1 + 1)
Down Arrow
d(54202324) = (3)(2)(2)(2)(2)
Down Arrow
d(54202324) = 48

More numbers for you to try

Take a look at the factors page to see the factors of 54,202,324 and how to find them.

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