Q: What is the total or count of factors of the number 788,480?

 A: 96

How do I find the total factors of the number 788,480?

Step 1

Find the prime factorization of the number 788,480.

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

Factor Tree
788,480
Factor Arrows
2394,240
Factor Arrows
2197,120
Factor Arrows
298,560
Factor Arrows
249,280
Factor Arrows
224,640
Factor Arrows
212,320
Factor Arrows
26,160
Factor Arrows
23,080
Factor Arrows
21,540
Factor Arrows
2770
Factor Arrows
2385
Factor Arrows
577
Factor Arrows
711

The prime factorization in exponential form is: 211 x 51 x 71 x 111

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.

788,480 = 211 x 51 x 71 x 111
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)(d + 1)
Down Arrow
d(788480) = (11 + 1)(1 + 1)(1 + 1)(1 + 1)
Down Arrow
d(788480) = (12)(2)(2)(2)
Down Arrow
d(788480) = 96

More numbers for you to try

Take a look at the factors page to see the factors of 788,480 and how to find them.

Try the factor calculator.

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