Q: What is the total or count of factors of the number 807,651?

 A: 30

How do I find the total factors of the number 807,651?

Step 1

Find the prime factorization of the number 807,651.

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

Factor Tree
807,651
Factor Arrows
3269,217
Factor Arrows
389,739
Factor Arrows
329,913
Factor Arrows
39,971
Factor Arrows
13767
Factor Arrows
1359

The prime factorization in exponential form is: 34 x 132 x 591

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.

807,651 = 34 x 132 x 591
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)
Down Arrow
d(807651) = (4 + 1)(2 + 1)(1 + 1)
Down Arrow
d(807651) = (5)(3)(2)
Down Arrow
d(807651) = 30

More numbers for you to try

Take a look at the factors page to see the factors of 807,651 and how to find them.

Try the factor calculator.

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