Q: What is the total or count of factors of the number 121,610,520?

 A: 192

How do I find the total factors of the number 121,610,520?

Step 1

Find the prime factorization of the number 121,610,520.

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

Factor Tree
121,610,520
Factor Arrows
260,805,260
Factor Arrows
230,402,630
Factor Arrows
215,201,315
Factor Arrows
35,067,105
Factor Arrows
31,689,035
Factor Arrows
5337,807
Factor Arrows
1719,871
Factor Arrows
31641

The prime factorization in exponential form is: 23 x 32 x 51 x 171 x 311 x 6411

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.

121,610,520 = 23 x 32 x 51 x 171 x 311 x 6411
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)(d + 1)(e + 1)(f + 1)
Down Arrow
d(121610520) = (3 + 1)(2 + 1)(1 + 1)(1 + 1)(1 + 1)(1 + 1)
Down Arrow
d(121610520) = (4)(3)(2)(2)(2)(2)
Down Arrow
d(121610520) = 192

More numbers for you to try

Take a look at the factors page to see the factors of 121,610,520 and how to find them.

Try the factor calculator.

Explore more about the number 121,610,520:


Ask a Question