Q: What is the total or count of factors of the number 480,249?

 A: 45

How do I find the total factors of the number 480,249?

Step 1

Find the prime factorization of the number 480,249.

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

Factor Tree
480,249
Factor Arrows
3160,083
Factor Arrows
353,361
Factor Arrows
317,787
Factor Arrows
35,929
Factor Arrows
7847
Factor Arrows
7121
Factor Arrows
1111

The prime factorization in exponential form is: 34 x 72 x 112

Step 2

Setup the equation for determining the number of factors or divisors. The equation is:

d(n) = (a + 1)(b + 1)(c + 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.

480,249 = 34 x 72 x 112
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)
Down Arrow
d(480249) = (4 + 1)(2 + 1)(2 + 1)
Down Arrow
d(480249) = (5)(3)(3)
Down Arrow
d(480249) = 45

More numbers for you to try

Take a look at the factors page to see the factors of 480,249 and how to find them.

Try the factor calculator.

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