Q: What is the total or count of factors of the number 23,013,120?

 A: 144

How do I find the total factors of the number 23,013,120?

Step 1

Find the prime factorization of the number 23,013,120.

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

Factor Tree
23,013,120
Factor Arrows
211,506,560
Factor Arrows
25,753,280
Factor Arrows
22,876,640
Factor Arrows
21,438,320
Factor Arrows
2719,160
Factor Arrows
2359,580
Factor Arrows
2179,790
Factor Arrows
289,895
Factor Arrows
329,965
Factor Arrows
55,993
Factor Arrows
13461

The prime factorization in exponential form is: 28 x 31 x 51 x 131 x 4611

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.

23,013,120 = 28 x 31 x 51 x 131 x 4611
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)(d + 1)(e + 1)
Down Arrow
d(23013120) = (8 + 1)(1 + 1)(1 + 1)(1 + 1)(1 + 1)
Down Arrow
d(23013120) = (9)(2)(2)(2)(2)
Down Arrow
d(23013120) = 144

More numbers for you to try

Take a look at the factors page to see the factors of 23,013,120 and how to find them.

Try the factor calculator.

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