Q: What is the total or count of factors of the number 183,624?

 A: 32

How do I find the total factors of the number 183,624?

Step 1

Find the prime factorization of the number 183,624.

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

Factor Tree
183,624
Factor Arrows
291,812
Factor Arrows
245,906
Factor Arrows
222,953
Factor Arrows
37,651
Factor Arrows
71,093

The prime factorization in exponential form is: 23 x 31 x 71 x 1,0931

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.

183,624 = 23 x 31 x 71 x 1,0931
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)(d + 1)
Down Arrow
d(183624) = (3 + 1)(1 + 1)(1 + 1)(1 + 1)
Down Arrow
d(183624) = (4)(2)(2)(2)
Down Arrow
d(183624) = 32

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Take a look at the factors page to see the factors of 183,624 and how to find them.

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