Q: What is the total or count of factors of the number 515,356,032?

 A: 192

How do I find the total factors of the number 515,356,032?

Step 1

Find the prime factorization of the number 515,356,032.

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

Factor Tree
515,356,032
Factor Arrows
2257,678,016
Factor Arrows
2128,839,008
Factor Arrows
264,419,504
Factor Arrows
232,209,752
Factor Arrows
216,104,876
Factor Arrows
28,052,438
Factor Arrows
24,026,219
Factor Arrows
31,342,073
Factor Arrows
2358,351
Factor Arrows
232,537
Factor Arrows
4359

The prime factorization in exponential form is: 27 x 31 x 232 x 431 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)(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.

515,356,032 = 27 x 31 x 232 x 431 x 591
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)(d + 1)(e + 1)
Down Arrow
d(515356032) = (7 + 1)(1 + 1)(2 + 1)(1 + 1)(1 + 1)
Down Arrow
d(515356032) = (8)(2)(3)(2)(2)
Down Arrow
d(515356032) = 192

More numbers for you to try

Take a look at the factors page to see the factors of 515,356,032 and how to find them.

Try the factor calculator.

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