Q: What is the total or count of factors of the number 83,415?

 A: 16

How do I find the total factors of the number 83,415?

Step 1

Find the prime factorization of the number 83,415.

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

Factor Tree
83,415
Factor Arrows
327,805
Factor Arrows
55,561
Factor Arrows
6783

The prime factorization in exponential form is: 31 x 51 x 671 x 831

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.

83,415 = 31 x 51 x 671 x 831
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)(d + 1)
Down Arrow
d(83415) = (1 + 1)(1 + 1)(1 + 1)(1 + 1)
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d(83415) = (2)(2)(2)(2)
Down Arrow
d(83415) = 16

More numbers for you to try

Take a look at the factors page to see the factors of 83,415 and how to find them.

Try the factor calculator.

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