Q: What is the total or count of factors of the number 183,360?

 A: 56

How do I find the total factors of the number 183,360?

Step 1

Find the prime factorization of the number 183,360.

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

Factor Tree
183,360
Factor Arrows
291,680
Factor Arrows
245,840
Factor Arrows
222,920
Factor Arrows
211,460
Factor Arrows
25,730
Factor Arrows
22,865
Factor Arrows
3955
Factor Arrows
5191

The prime factorization in exponential form is: 26 x 31 x 51 x 1911

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.

183,360 = 26 x 31 x 51 x 1911
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)(d + 1)
Down Arrow
d(183360) = (6 + 1)(1 + 1)(1 + 1)(1 + 1)
Down Arrow
d(183360) = (7)(2)(2)(2)
Down Arrow
d(183360) = 56

More numbers for you to try

Take a look at the factors page to see the factors of 183,360 and how to find them.

Try the factor calculator.

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