Q: What is the total or count of factors of the number 20,500?

 A: 24

How do I find the total factors of the number 20,500?

Step 1

Find the prime factorization of the number 20,500.

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

Factor Tree
20,500
Factor Arrows
210,250
Factor Arrows
25,125
Factor Arrows
51,025
Factor Arrows
5205
Factor Arrows
541

The prime factorization in exponential form is: 22 x 53 x 411

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.

20,500 = 22 x 53 x 411
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)
Down Arrow
d(20500) = (2 + 1)(3 + 1)(1 + 1)
Down Arrow
d(20500) = (3)(4)(2)
Down Arrow
d(20500) = 24

More numbers for you to try

Take a look at the factors page to see the factors of 20,500 and how to find them.

Try the factor calculator.

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