Q: What is the total or count of factors of the number 305,123,200?

 A: 96

How do I find the total factors of the number 305,123,200?

Step 1

Find the prime factorization of the number 305,123,200.

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

Factor Tree
305,123,200
Factor Arrows
2152,561,600
Factor Arrows
276,280,800
Factor Arrows
238,140,400
Factor Arrows
219,070,200
Factor Arrows
29,535,100
Factor Arrows
24,767,550
Factor Arrows
22,383,775
Factor Arrows
5476,755
Factor Arrows
595,351
Factor Arrows
97983

The prime factorization in exponential form is: 27 x 52 x 971 x 9831

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.

305,123,200 = 27 x 52 x 971 x 9831
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)(d + 1)
Down Arrow
d(305123200) = (7 + 1)(2 + 1)(1 + 1)(1 + 1)
Down Arrow
d(305123200) = (8)(3)(2)(2)
Down Arrow
d(305123200) = 96

More numbers for you to try

Take a look at the factors page to see the factors of 305,123,200 and how to find them.

Try the factor calculator.

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