Q: What is the total or count of factors of the number 827,928?

 A: 32

How do I find the total factors of the number 827,928?

Step 1

Find the prime factorization of the number 827,928.

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

Factor Tree
827,928
Factor Arrows
2413,964
Factor Arrows
2206,982
Factor Arrows
2103,491
Factor Arrows
334,497
Factor Arrows
311,499
Factor Arrows
33,833

The prime factorization in exponential form is: 23 x 33 x 3,8331

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.

827,928 = 23 x 33 x 3,8331
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)
Down Arrow
d(827928) = (3 + 1)(3 + 1)(1 + 1)
Down Arrow
d(827928) = (4)(4)(2)
Down Arrow
d(827928) = 32

More numbers for you to try

Take a look at the factors page to see the factors of 827,928 and how to find them.

Try the factor calculator.

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