Q: What is the total or count of factors of the number 21,300,720?

 A: 160

How do I find the total factors of the number 21,300,720?

Step 1

Find the prime factorization of the number 21,300,720.

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

Factor Tree
21,300,720
Factor Arrows
210,650,360
Factor Arrows
25,325,180
Factor Arrows
22,662,590
Factor Arrows
21,331,295
Factor Arrows
3443,765
Factor Arrows
588,753
Factor Arrows
712,679
Factor Arrows
31409

The prime factorization in exponential form is: 24 x 31 x 51 x 71 x 311 x 4091

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.

21,300,720 = 24 x 31 x 51 x 71 x 311 x 4091
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)(d + 1)(e + 1)(f + 1)
Down Arrow
d(21300720) = (4 + 1)(1 + 1)(1 + 1)(1 + 1)(1 + 1)(1 + 1)
Down Arrow
d(21300720) = (5)(2)(2)(2)(2)(2)
Down Arrow
d(21300720) = 160

More numbers for you to try

Take a look at the factors page to see the factors of 21,300,720 and how to find them.

Try the factor calculator.

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