Q: What is the total or count of factors of the number 259,290?

 A: 48

How do I find the total factors of the number 259,290?

Step 1

Find the prime factorization of the number 259,290.

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

Factor Tree
259,290
Factor Arrows
2129,645
Factor Arrows
343,215
Factor Arrows
314,405
Factor Arrows
52,881
Factor Arrows
4367

The prime factorization in exponential form is: 21 x 32 x 51 x 431 x 671

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.

259,290 = 21 x 32 x 51 x 431 x 671
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)(d + 1)(e + 1)
Down Arrow
d(259290) = (1 + 1)(2 + 1)(1 + 1)(1 + 1)(1 + 1)
Down Arrow
d(259290) = (2)(3)(2)(2)(2)
Down Arrow
d(259290) = 48

More numbers for you to try

Take a look at the factors page to see the factors of 259,290 and how to find them.

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