Q: What is the total or count of factors of the number 86,528?

 A: 30

How do I find the total factors of the number 86,528?

Step 1

Find the prime factorization of the number 86,528.

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

Factor Tree
86,528
Factor Arrows
243,264
Factor Arrows
221,632
Factor Arrows
210,816
Factor Arrows
25,408
Factor Arrows
22,704
Factor Arrows
21,352
Factor Arrows
2676
Factor Arrows
2338
Factor Arrows
2169
Factor Arrows
1313

The prime factorization in exponential form is: 29 x 132

Step 2

Setup the equation for determining the number of factors or divisors. The equation is:

d(n) = (a + 1)(b + 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.

86,528 = 29 x 132
Down Arrow
d(n) = (a + 1)(b + 1)
Down Arrow
d(86528) = (9 + 1)(2 + 1)
Down Arrow
d(86528) = (10)(3)
Down Arrow
d(86528) = 30

More numbers for you to try

Take a look at the factors page to see the factors of 86,528 and how to find them.

Try the factor calculator.

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