Q: What is the total or count of factors of the number 500,314,353?

 A: 48

How do I find the total factors of the number 500,314,353?

Step 1

Find the prime factorization of the number 500,314,353.

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

Factor Tree
500,314,353
Factor Arrows
3166,771,451
Factor Arrows
723,824,493
Factor Arrows
73,403,499
Factor Arrows
11309,409
Factor Arrows
2771,117

The prime factorization in exponential form is: 31 x 72 x 111 x 2771 x 1,1171

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)(e + 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.

500,314,353 = 31 x 72 x 111 x 2771 x 1,1171
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)(d + 1)(e + 1)
Down Arrow
d(500314353) = (1 + 1)(2 + 1)(1 + 1)(1 + 1)(1 + 1)
Down Arrow
d(500314353) = (2)(3)(2)(2)(2)
Down Arrow
d(500314353) = 48

More numbers for you to try

Take a look at the factors page to see the factors of 500,314,353 and how to find them.

Try the factor calculator.

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