Q: What is the total or count of factors of the number 514,615,640?

 A: 96

How do I find the total factors of the number 514,615,640?

Step 1

Find the prime factorization of the number 514,615,640.

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

Factor Tree
514,615,640
Factor Arrows
2257,307,820
Factor Arrows
2128,653,910
Factor Arrows
264,326,955
Factor Arrows
512,865,391
Factor Arrows
71,837,913
Factor Arrows
7262,559
Factor Arrows
1123,869

The prime factorization in exponential form is: 23 x 51 x 72 x 111 x 23,8691

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.

514,615,640 = 23 x 51 x 72 x 111 x 23,8691
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)(d + 1)(e + 1)
Down Arrow
d(514615640) = (3 + 1)(1 + 1)(2 + 1)(1 + 1)(1 + 1)
Down Arrow
d(514615640) = (4)(2)(3)(2)(2)
Down Arrow
d(514615640) = 96

More numbers for you to try

Take a look at the factors page to see the factors of 514,615,640 and how to find them.

Try the factor calculator.

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