Q: What is the total or count of factors of the number 54,243,123?

 A: 32

How do I find the total factors of the number 54,243,123?

Step 1

Find the prime factorization of the number 54,243,123.

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

Factor Tree
54,243,123
Factor Arrows
318,081,041
Factor Arrows
111,643,731
Factor Arrows
4140,091
Factor Arrows
47853

The prime factorization in exponential form is: 31 x 111 x 411 x 471 x 8531

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.

54,243,123 = 31 x 111 x 411 x 471 x 8531
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)(d + 1)(e + 1)
Down Arrow
d(54243123) = (1 + 1)(1 + 1)(1 + 1)(1 + 1)(1 + 1)
Down Arrow
d(54243123) = (2)(2)(2)(2)(2)
Down Arrow
d(54243123) = 32

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Take a look at the factors page to see the factors of 54,243,123 and how to find them.

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