Q: What is the total or count of factors of the number 590,304?

 A: 96

How do I find the total factors of the number 590,304?

Step 1

Find the prime factorization of the number 590,304.

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

Factor Tree
590,304
Factor Arrows
2295,152
Factor Arrows
2147,576
Factor Arrows
273,788
Factor Arrows
236,894
Factor Arrows
218,447
Factor Arrows
36,149
Factor Arrows
11559
Factor Arrows
1343

The prime factorization in exponential form is: 25 x 31 x 111 x 131 x 431

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.

590,304 = 25 x 31 x 111 x 131 x 431
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)(d + 1)(e + 1)
Down Arrow
d(590304) = (5 + 1)(1 + 1)(1 + 1)(1 + 1)(1 + 1)
Down Arrow
d(590304) = (6)(2)(2)(2)(2)
Down Arrow
d(590304) = 96

More numbers for you to try

Take a look at the factors page to see the factors of 590,304 and how to find them.

Try the factor calculator.

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