Q: What is the total or count of factors of the number 367,952?

 A: 40

How do I find the total factors of the number 367,952?

Step 1

Find the prime factorization of the number 367,952.

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

Factor Tree
367,952
Factor Arrows
2183,976
Factor Arrows
291,988
Factor Arrows
245,994
Factor Arrows
222,997
Factor Arrows
131,769
Factor Arrows
2961

The prime factorization in exponential form is: 24 x 131 x 291 x 611

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.

367,952 = 24 x 131 x 291 x 611
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)(d + 1)
Down Arrow
d(367952) = (4 + 1)(1 + 1)(1 + 1)(1 + 1)
Down Arrow
d(367952) = (5)(2)(2)(2)
Down Arrow
d(367952) = 40

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Take a look at the factors page to see the factors of 367,952 and how to find them.

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