Q: What is the total or count of factors of the number 725,227,256?

 A: 32

How do I find the total factors of the number 725,227,256?

Step 1

Find the prime factorization of the number 725,227,256.

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

Factor Tree
725,227,256
Factor Arrows
2362,613,628
Factor Arrows
2181,306,814
Factor Arrows
290,653,407
Factor Arrows
136,973,339
Factor Arrows
21133,049

The prime factorization in exponential form is: 23 x 131 x 2111 x 33,0491

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.

725,227,256 = 23 x 131 x 2111 x 33,0491
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)(d + 1)
Down Arrow
d(725227256) = (3 + 1)(1 + 1)(1 + 1)(1 + 1)
Down Arrow
d(725227256) = (4)(2)(2)(2)
Down Arrow
d(725227256) = 32

More numbers for you to try

Take a look at the factors page to see the factors of 725,227,256 and how to find them.

Try the factor calculator.

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