Q: What is the total or count of factors of the number 788,096?

 A: 32

How do I find the total factors of the number 788,096?

Step 1

Find the prime factorization of the number 788,096.

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

Factor Tree
788,096
Factor Arrows
2394,048
Factor Arrows
2197,024
Factor Arrows
298,512
Factor Arrows
249,256
Factor Arrows
224,628
Factor Arrows
212,314
Factor Arrows
26,157
Factor Arrows
47131

The prime factorization in exponential form is: 27 x 471 x 1311

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.

788,096 = 27 x 471 x 1311
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)
Down Arrow
d(788096) = (7 + 1)(1 + 1)(1 + 1)
Down Arrow
d(788096) = (8)(2)(2)
Down Arrow
d(788096) = 32

More numbers for you to try

Take a look at the factors page to see the factors of 788,096 and how to find them.

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