Q: What is the total or count of factors of the number 20,462,640?

 A: 160

How do I find the total factors of the number 20,462,640?

Step 1

Find the prime factorization of the number 20,462,640.

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

Factor Tree
20,462,640
Factor Arrows
210,231,320
Factor Arrows
25,115,660
Factor Arrows
22,557,830
Factor Arrows
21,278,915
Factor Arrows
3426,305
Factor Arrows
585,261
Factor Arrows
117,751
Factor Arrows
23337

The prime factorization in exponential form is: 24 x 31 x 51 x 111 x 231 x 3371

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.

20,462,640 = 24 x 31 x 51 x 111 x 231 x 3371
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)(d + 1)(e + 1)(f + 1)
Down Arrow
d(20462640) = (4 + 1)(1 + 1)(1 + 1)(1 + 1)(1 + 1)(1 + 1)
Down Arrow
d(20462640) = (5)(2)(2)(2)(2)(2)
Down Arrow
d(20462640) = 160

More numbers for you to try

Take a look at the factors page to see the factors of 20,462,640 and how to find them.

Try the factor calculator.

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