Q: What is the total or count of factors of the number 35,100?

 A: 72

How do I find the total factors of the number 35,100?

Step 1

Find the prime factorization of the number 35,100.

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

Factor Tree
35,100
Factor Arrows
217,550
Factor Arrows
28,775
Factor Arrows
32,925
Factor Arrows
3975
Factor Arrows
3325
Factor Arrows
565
Factor Arrows
513

The prime factorization in exponential form is: 22 x 33 x 52 x 131

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.

35,100 = 22 x 33 x 52 x 131
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)(d + 1)
Down Arrow
d(35100) = (2 + 1)(3 + 1)(2 + 1)(1 + 1)
Down Arrow
d(35100) = (3)(4)(3)(2)
Down Arrow
d(35100) = 72

More numbers for you to try

Take a look at the factors page to see the factors of 35,100 and how to find them.

Try the factor calculator.

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