Q: What is the total or count of factors of the number 34,215,444?

 A: 108

How do I find the total factors of the number 34,215,444?

Step 1

Find the prime factorization of the number 34,215,444.

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

Factor Tree
34,215,444
Factor Arrows
217,107,722
Factor Arrows
28,553,861
Factor Arrows
32,851,287
Factor Arrows
3950,429
Factor Arrows
2341,323
Factor Arrows
311,333
Factor Arrows
3143

The prime factorization in exponential form is: 22 x 32 x 231 x 312 x 431

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.

34,215,444 = 22 x 32 x 231 x 312 x 431
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)(d + 1)(e + 1)
Down Arrow
d(34215444) = (2 + 1)(2 + 1)(1 + 1)(2 + 1)(1 + 1)
Down Arrow
d(34215444) = (3)(3)(2)(3)(2)
Down Arrow
d(34215444) = 108

More numbers for you to try

Take a look at the factors page to see the factors of 34,215,444 and how to find them.

Try the factor calculator.

Explore more about the number 34,215,444:


Ask a Question