Q: What is the total or count of factors of the number 165,900?

 A: 72

How do I find the total factors of the number 165,900?

Step 1

Find the prime factorization of the number 165,900.

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

Factor Tree
165,900
Factor Arrows
282,950
Factor Arrows
241,475
Factor Arrows
313,825
Factor Arrows
52,765
Factor Arrows
5553
Factor Arrows
779

The prime factorization in exponential form is: 22 x 31 x 52 x 71 x 791

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)(e + 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.

165,900 = 22 x 31 x 52 x 71 x 791
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)(d + 1)(e + 1)
Down Arrow
d(165900) = (2 + 1)(1 + 1)(2 + 1)(1 + 1)(1 + 1)
Down Arrow
d(165900) = (3)(2)(3)(2)(2)
Down Arrow
d(165900) = 72

More numbers for you to try

Take a look at the factors page to see the factors of 165,900 and how to find them.

Try the factor calculator.

Explore more about the number 165,900:


Ask a Question