Q: What is the total or count of factors of the number 362,352?

 A: 20

How do I find the total factors of the number 362,352?

Step 1

Find the prime factorization of the number 362,352.

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

Factor Tree
362,352
Factor Arrows
2181,176
Factor Arrows
290,588
Factor Arrows
245,294
Factor Arrows
222,647
Factor Arrows
37,549

The prime factorization in exponential form is: 24 x 31 x 7,5491

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.

362,352 = 24 x 31 x 7,5491
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)
Down Arrow
d(362352) = (4 + 1)(1 + 1)(1 + 1)
Down Arrow
d(362352) = (5)(2)(2)
Down Arrow
d(362352) = 20

More numbers for you to try

Take a look at the factors page to see the factors of 362,352 and how to find them.

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