Q: What is the total or count of factors of the number 864,384?

 A: 32

How do I find the total factors of the number 864,384?

Step 1

Find the prime factorization of the number 864,384.

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

Factor Tree
864,384
Factor Arrows
2432,192
Factor Arrows
2216,096
Factor Arrows
2108,048
Factor Arrows
254,024
Factor Arrows
227,012
Factor Arrows
213,506
Factor Arrows
26,753
Factor Arrows
32,251

The prime factorization in exponential form is: 27 x 31 x 2,2511

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.

864,384 = 27 x 31 x 2,2511
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)
Down Arrow
d(864384) = (7 + 1)(1 + 1)(1 + 1)
Down Arrow
d(864384) = (8)(2)(2)
Down Arrow
d(864384) = 32

More numbers for you to try

Take a look at the factors page to see the factors of 864,384 and how to find them.

Try the factor calculator.

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