Q: What is the total or count of factors of the number 198,156?

 A: 36

How do I find the total factors of the number 198,156?

Step 1

Find the prime factorization of the number 198,156.

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

Factor Tree
198,156
Factor Arrows
299,078
Factor Arrows
249,539
Factor Arrows
316,513
Factor Arrows
72,359
Factor Arrows
7337

The prime factorization in exponential form is: 22 x 31 x 72 x 3371

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.

198,156 = 22 x 31 x 72 x 3371
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)(d + 1)
Down Arrow
d(198156) = (2 + 1)(1 + 1)(2 + 1)(1 + 1)
Down Arrow
d(198156) = (3)(2)(3)(2)
Down Arrow
d(198156) = 36

More numbers for you to try

Take a look at the factors page to see the factors of 198,156 and how to find them.

Try the factor calculator.

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