Q: What is the total or count of factors of the number 226,138?

 A: 16

How do I find the total factors of the number 226,138?

Step 1

Find the prime factorization of the number 226,138.

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

Factor Tree
226,138
Factor Arrows
2113,069
Factor Arrows
1110,279
Factor Arrows
19541

The prime factorization in exponential form is: 21 x 111 x 191 x 5411

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.

226,138 = 21 x 111 x 191 x 5411
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)(d + 1)
Down Arrow
d(226138) = (1 + 1)(1 + 1)(1 + 1)(1 + 1)
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d(226138) = (2)(2)(2)(2)
Down Arrow
d(226138) = 16

More numbers for you to try

Take a look at the factors page to see the factors of 226,138 and how to find them.

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