Q: What is the total or count of factors of the number 20,413,600?

 A: 144

How do I find the total factors of the number 20,413,600?

Step 1

Find the prime factorization of the number 20,413,600.

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

Factor Tree
20,413,600
Factor Arrows
210,206,800
Factor Arrows
25,103,400
Factor Arrows
22,551,700
Factor Arrows
21,275,850
Factor Arrows
2637,925
Factor Arrows
5127,585
Factor Arrows
525,517
Factor Arrows
171,501
Factor Arrows
1979

The prime factorization in exponential form is: 25 x 52 x 171 x 191 x 791

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.

20,413,600 = 25 x 52 x 171 x 191 x 791
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)(d + 1)(e + 1)
Down Arrow
d(20413600) = (5 + 1)(2 + 1)(1 + 1)(1 + 1)(1 + 1)
Down Arrow
d(20413600) = (6)(3)(2)(2)(2)
Down Arrow
d(20413600) = 144

More numbers for you to try

Take a look at the factors page to see the factors of 20,413,600 and how to find them.

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