Q: What is the total or count of factors of the number 320,100?

 A: 72

How do I find the total factors of the number 320,100?

Step 1

Find the prime factorization of the number 320,100.

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

Factor Tree
320,100
Factor Arrows
2160,050
Factor Arrows
280,025
Factor Arrows
326,675
Factor Arrows
55,335
Factor Arrows
51,067
Factor Arrows
1197

The prime factorization in exponential form is: 22 x 31 x 52 x 111 x 971

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.

320,100 = 22 x 31 x 52 x 111 x 971
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)(d + 1)(e + 1)
Down Arrow
d(320100) = (2 + 1)(1 + 1)(2 + 1)(1 + 1)(1 + 1)
Down Arrow
d(320100) = (3)(2)(3)(2)(2)
Down Arrow
d(320100) = 72

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Take a look at the factors page to see the factors of 320,100 and how to find them.

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