Q: What is the total or count of factors of the number 54,177,504?

 A: 96

How do I find the total factors of the number 54,177,504?

Step 1

Find the prime factorization of the number 54,177,504.

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

Factor Tree
54,177,504
Factor Arrows
227,088,752
Factor Arrows
213,544,376
Factor Arrows
26,772,188
Factor Arrows
23,386,094
Factor Arrows
21,693,047
Factor Arrows
3564,349
Factor Arrows
1733,197
Factor Arrows
89373

The prime factorization in exponential form is: 25 x 31 x 171 x 891 x 3731

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.

54,177,504 = 25 x 31 x 171 x 891 x 3731
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)(d + 1)(e + 1)
Down Arrow
d(54177504) = (5 + 1)(1 + 1)(1 + 1)(1 + 1)(1 + 1)
Down Arrow
d(54177504) = (6)(2)(2)(2)(2)
Down Arrow
d(54177504) = 96

More numbers for you to try

Take a look at the factors page to see the factors of 54,177,504 and how to find them.

Try the factor calculator.

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