Q: What is the total or count of factors of the number 170,200?

 A: 48

How do I find the total factors of the number 170,200?

Step 1

Find the prime factorization of the number 170,200.

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

Factor Tree
170,200
Factor Arrows
285,100
Factor Arrows
242,550
Factor Arrows
221,275
Factor Arrows
54,255
Factor Arrows
5851
Factor Arrows
2337

The prime factorization in exponential form is: 23 x 52 x 231 x 371

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.

170,200 = 23 x 52 x 231 x 371
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)(d + 1)
Down Arrow
d(170200) = (3 + 1)(2 + 1)(1 + 1)(1 + 1)
Down Arrow
d(170200) = (4)(3)(2)(2)
Down Arrow
d(170200) = 48

More numbers for you to try

Take a look at the factors page to see the factors of 170,200 and how to find them.

Try the factor calculator.

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