Q: What is the total or count of factors of the number 20,744,640?

 A: 280

How do I find the total factors of the number 20,744,640?

Step 1

Find the prime factorization of the number 20,744,640.

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

Factor Tree
20,744,640
Factor Arrows
210,372,320
Factor Arrows
25,186,160
Factor Arrows
22,593,080
Factor Arrows
21,296,540
Factor Arrows
2648,270
Factor Arrows
2324,135
Factor Arrows
3108,045
Factor Arrows
336,015
Factor Arrows
312,005
Factor Arrows
52,401
Factor Arrows
7343
Factor Arrows
749
Factor Arrows
77

The prime factorization in exponential form is: 26 x 33 x 51 x 74

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)

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.

20,744,640 = 26 x 33 x 51 x 74
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)(d + 1)
Down Arrow
d(20744640) = (6 + 1)(3 + 1)(1 + 1)(4 + 1)
Down Arrow
d(20744640) = (7)(4)(2)(5)
Down Arrow
d(20744640) = 280

More numbers for you to try

Take a look at the factors page to see the factors of 20,744,640 and how to find them.

Try the factor calculator.

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