Q: What is the total or count of factors of the number 586,644?

 A: 48

How do I find the total factors of the number 586,644?

Step 1

Find the prime factorization of the number 586,644.

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

Factor Tree
586,644
Factor Arrows
2293,322
Factor Arrows
2146,661
Factor Arrows
348,887
Factor Arrows
192,573
Factor Arrows
3183

The prime factorization in exponential form is: 22 x 31 x 191 x 311 x 831

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.

586,644 = 22 x 31 x 191 x 311 x 831
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)(d + 1)(e + 1)
Down Arrow
d(586644) = (2 + 1)(1 + 1)(1 + 1)(1 + 1)(1 + 1)
Down Arrow
d(586644) = (3)(2)(2)(2)(2)
Down Arrow
d(586644) = 48

More numbers for you to try

Take a look at the factors page to see the factors of 586,644 and how to find them.

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