Q: What is the total or count of factors of the number 54,900?

 A: 54

How do I find the total factors of the number 54,900?

Step 1

Find the prime factorization of the number 54,900.

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

Factor Tree
54,900
Factor Arrows
227,450
Factor Arrows
213,725
Factor Arrows
34,575
Factor Arrows
31,525
Factor Arrows
5305
Factor Arrows
561

The prime factorization in exponential form is: 22 x 32 x 52 x 611

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.

54,900 = 22 x 32 x 52 x 611
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)(d + 1)
Down Arrow
d(54900) = (2 + 1)(2 + 1)(2 + 1)(1 + 1)
Down Arrow
d(54900) = (3)(3)(3)(2)
Down Arrow
d(54900) = 54

More numbers for you to try

Take a look at the factors page to see the factors of 54,900 and how to find them.

Try the factor calculator.

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