Q: What is the total or count of factors of the number 185,696?

 A: 24

How do I find the total factors of the number 185,696?

Step 1

Find the prime factorization of the number 185,696.

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

Factor Tree
185,696
Factor Arrows
292,848
Factor Arrows
246,424
Factor Arrows
223,212
Factor Arrows
211,606
Factor Arrows
25,803
Factor Arrows
7829

The prime factorization in exponential form is: 25 x 71 x 8291

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.

185,696 = 25 x 71 x 8291
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)
Down Arrow
d(185696) = (5 + 1)(1 + 1)(1 + 1)
Down Arrow
d(185696) = (6)(2)(2)
Down Arrow
d(185696) = 24

More numbers for you to try

Take a look at the factors page to see the factors of 185,696 and how to find them.

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