Q: What is the total or count of factors of the number 20,113,200?

 A: 180

How do I find the total factors of the number 20,113,200?

Step 1

Find the prime factorization of the number 20,113,200.

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

Factor Tree
20,113,200
Factor Arrows
210,056,600
Factor Arrows
25,028,300
Factor Arrows
22,514,150
Factor Arrows
21,257,075
Factor Arrows
3419,025
Factor Arrows
3139,675
Factor Arrows
527,935
Factor Arrows
55,587
Factor Arrows
37151

The prime factorization in exponential form is: 24 x 32 x 52 x 371 x 1511

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.

20,113,200 = 24 x 32 x 52 x 371 x 1511
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)(d + 1)(e + 1)
Down Arrow
d(20113200) = (4 + 1)(2 + 1)(2 + 1)(1 + 1)(1 + 1)
Down Arrow
d(20113200) = (5)(3)(3)(2)(2)
Down Arrow
d(20113200) = 180

More numbers for you to try

Take a look at the factors page to see the factors of 20,113,200 and how to find them.

Try the factor calculator.

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