Q: What is the total or count of factors of the number 323,111,100?

 A: 108

How do I find the total factors of the number 323,111,100?

Step 1

Find the prime factorization of the number 323,111,100.

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

Factor Tree
323,111,100
Factor Arrows
2161,555,550
Factor Arrows
280,777,775
Factor Arrows
326,925,925
Factor Arrows
55,385,185
Factor Arrows
51,077,037
Factor Arrows
1382,849
Factor Arrows
136,373

The prime factorization in exponential form is: 22 x 31 x 52 x 132 x 6,3731

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.

323,111,100 = 22 x 31 x 52 x 132 x 6,3731
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d(n) = (a + 1)(b + 1)(c + 1)(d + 1)(e + 1)
Down Arrow
d(323111100) = (2 + 1)(1 + 1)(2 + 1)(2 + 1)(1 + 1)
Down Arrow
d(323111100) = (3)(2)(3)(3)(2)
Down Arrow
d(323111100) = 108

More numbers for you to try

Take a look at the factors page to see the factors of 323,111,100 and how to find them.

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