Q: What is the total or count of factors of the number 504,334,400?

 A: 84

How do I find the total factors of the number 504,334,400?

Step 1

Find the prime factorization of the number 504,334,400.

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

Factor Tree
504,334,400
Factor Arrows
2252,167,200
Factor Arrows
2126,083,600
Factor Arrows
263,041,800
Factor Arrows
231,520,900
Factor Arrows
215,760,450
Factor Arrows
27,880,225
Factor Arrows
51,576,045
Factor Arrows
5315,209
Factor Arrows
383823

The prime factorization in exponential form is: 26 x 52 x 3831 x 8231

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.

504,334,400 = 26 x 52 x 3831 x 8231
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)(d + 1)
Down Arrow
d(504334400) = (6 + 1)(2 + 1)(1 + 1)(1 + 1)
Down Arrow
d(504334400) = (7)(3)(2)(2)
Down Arrow
d(504334400) = 84

More numbers for you to try

Take a look at the factors page to see the factors of 504,334,400 and how to find them.

Try the factor calculator.

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