Q: What is the total or count of factors of the number 364,080?

 A: 80

How do I find the total factors of the number 364,080?

Step 1

Find the prime factorization of the number 364,080.

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

Factor Tree
364,080
Factor Arrows
2182,040
Factor Arrows
291,020
Factor Arrows
245,510
Factor Arrows
222,755
Factor Arrows
37,585
Factor Arrows
51,517
Factor Arrows
3741

The prime factorization in exponential form is: 24 x 31 x 51 x 371 x 411

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.

364,080 = 24 x 31 x 51 x 371 x 411
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)(d + 1)(e + 1)
Down Arrow
d(364080) = (4 + 1)(1 + 1)(1 + 1)(1 + 1)(1 + 1)
Down Arrow
d(364080) = (5)(2)(2)(2)(2)
Down Arrow
d(364080) = 80

More numbers for you to try

Take a look at the factors page to see the factors of 364,080 and how to find them.

Try the factor calculator.

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