Q: What is the total or count of factors of the number 218,596?

 A: 24

How do I find the total factors of the number 218,596?

Step 1

Find the prime factorization of the number 218,596.

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

Factor Tree
218,596
Factor Arrows
2109,298
Factor Arrows
254,649
Factor Arrows
77,807
Factor Arrows
37211

The prime factorization in exponential form is: 22 x 71 x 371 x 2111

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.

218,596 = 22 x 71 x 371 x 2111
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)(d + 1)
Down Arrow
d(218596) = (2 + 1)(1 + 1)(1 + 1)(1 + 1)
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d(218596) = (3)(2)(2)(2)
Down Arrow
d(218596) = 24

More numbers for you to try

Take a look at the factors page to see the factors of 218,596 and how to find them.

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