Q: What is the total or count of factors of the number 122,331,300?

 A: 144

How do I find the total factors of the number 122,331,300?

Step 1

Find the prime factorization of the number 122,331,300.

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

Factor Tree
122,331,300
Factor Arrows
261,165,650
Factor Arrows
230,582,825
Factor Arrows
310,194,275
Factor Arrows
52,038,855
Factor Arrows
5407,771
Factor Arrows
758,253
Factor Arrows
134,481

The prime factorization in exponential form is: 22 x 31 x 52 x 71 x 131 x 4,4811

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)(f + 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.

122,331,300 = 22 x 31 x 52 x 71 x 131 x 4,4811
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)(d + 1)(e + 1)(f + 1)
Down Arrow
d(122331300) = (2 + 1)(1 + 1)(2 + 1)(1 + 1)(1 + 1)(1 + 1)
Down Arrow
d(122331300) = (3)(2)(3)(2)(2)(2)
Down Arrow
d(122331300) = 144

More numbers for you to try

Take a look at the factors page to see the factors of 122,331,300 and how to find them.

Try the factor calculator.

Explore more about the number 122,331,300:


Ask a Question