Q: What is the total or count of factors of the number 30,129,489?

 A: 60

How do I find the total factors of the number 30,129,489?

Step 1

Find the prime factorization of the number 30,129,489.

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

Factor Tree
30,129,489
Factor Arrows
310,043,163
Factor Arrows
33,347,721
Factor Arrows
31,115,907
Factor Arrows
3371,969
Factor Arrows
1328,613
Factor Arrows
132,201
Factor Arrows
3171

The prime factorization in exponential form is: 34 x 132 x 311 x 711

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.

30,129,489 = 34 x 132 x 311 x 711
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)(d + 1)
Down Arrow
d(30129489) = (4 + 1)(2 + 1)(1 + 1)(1 + 1)
Down Arrow
d(30129489) = (5)(3)(2)(2)
Down Arrow
d(30129489) = 60

More numbers for you to try

Take a look at the factors page to see the factors of 30,129,489 and how to find them.

Try the factor calculator.

Explore more about the number 30,129,489:


Ask a Question