Q: What is the total or count of factors of the number 202,222,020?

 A: 432

How do I find the total factors of the number 202,222,020?

Step 1

Find the prime factorization of the number 202,222,020.

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

Factor Tree
202,222,020
Factor Arrows
2101,111,010
Factor Arrows
250,555,505
Factor Arrows
316,851,835
Factor Arrows
53,370,367
Factor Arrows
7481,481
Factor Arrows
768,783
Factor Arrows
116,253
Factor Arrows
13481
Factor Arrows
1337

The prime factorization in exponential form is: 22 x 31 x 51 x 72 x 111 x 132 x 371

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)(g + 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.

202,222,020 = 22 x 31 x 51 x 72 x 111 x 132 x 371
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)(d + 1)(e + 1)(f + 1)(g + 1)
Down Arrow
d(202222020) = (2 + 1)(1 + 1)(1 + 1)(2 + 1)(1 + 1)(2 + 1)(1 + 1)
Down Arrow
d(202222020) = (3)(2)(2)(3)(2)(3)(2)
Down Arrow
d(202222020) = 432

More numbers for you to try

Take a look at the factors page to see the factors of 202,222,020 and how to find them.

Try the factor calculator.

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