Q: What is the total or count of factors of the number 390,504?

 A: 32

How do I find the total factors of the number 390,504?

Step 1

Find the prime factorization of the number 390,504.

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

Factor Tree
390,504
Factor Arrows
2195,252
Factor Arrows
297,626
Factor Arrows
248,813
Factor Arrows
316,271
Factor Arrows
53307

The prime factorization in exponential form is: 23 x 31 x 531 x 3071

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.

390,504 = 23 x 31 x 531 x 3071
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)(d + 1)
Down Arrow
d(390504) = (3 + 1)(1 + 1)(1 + 1)(1 + 1)
Down Arrow
d(390504) = (4)(2)(2)(2)
Down Arrow
d(390504) = 32

More numbers for you to try

Take a look at the factors page to see the factors of 390,504 and how to find them.

Try the factor calculator.

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