Q: What is the total or count of factors of the number 104,004,225?

 A: 108

How do I find the total factors of the number 104,004,225?

Step 1

Find the prime factorization of the number 104,004,225.

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

Factor Tree
104,004,225
Factor Arrows
334,668,075
Factor Arrows
311,556,025
Factor Arrows
52,311,205
Factor Arrows
5462,241
Factor Arrows
1335,557
Factor Arrows
311,147
Factor Arrows
3137

The prime factorization in exponential form is: 32 x 52 x 131 x 312 x 371

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.

104,004,225 = 32 x 52 x 131 x 312 x 371
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)(d + 1)(e + 1)
Down Arrow
d(104004225) = (2 + 1)(2 + 1)(1 + 1)(2 + 1)(1 + 1)
Down Arrow
d(104004225) = (3)(3)(2)(3)(2)
Down Arrow
d(104004225) = 108

More numbers for you to try

Take a look at the factors page to see the factors of 104,004,225 and how to find them.

Try the factor calculator.

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