Q: What is the total or count of factors of the number 204,612,224?

 A: 32

How do I find the total factors of the number 204,612,224?

Step 1

Find the prime factorization of the number 204,612,224.

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

Factor Tree
204,612,224
Factor Arrows
2102,306,112
Factor Arrows
251,153,056
Factor Arrows
225,576,528
Factor Arrows
212,788,264
Factor Arrows
26,394,132
Factor Arrows
23,197,066
Factor Arrows
21,598,533
Factor Arrows
5330,161

The prime factorization in exponential form is: 27 x 531 x 30,1611

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.

204,612,224 = 27 x 531 x 30,1611
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)
Down Arrow
d(204612224) = (7 + 1)(1 + 1)(1 + 1)
Down Arrow
d(204612224) = (8)(2)(2)
Down Arrow
d(204612224) = 32

More numbers for you to try

Take a look at the factors page to see the factors of 204,612,224 and how to find them.

Try the factor calculator.

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