Q: What is the total or count of factors of the number 138,424?

 A: 32

How do I find the total factors of the number 138,424?

Step 1

Find the prime factorization of the number 138,424.

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

Factor Tree
138,424
Factor Arrows
269,212
Factor Arrows
234,606
Factor Arrows
217,303
Factor Arrows
111,573
Factor Arrows
11143
Factor Arrows
1113

The prime factorization in exponential form is: 23 x 113 x 131

Step 2

Setup the equation for determining the number of factors or divisors. The equation is:

d(n) = (a + 1)(b + 1)(c + 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.

138,424 = 23 x 113 x 131
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d(n) = (a + 1)(b + 1)(c + 1)
Down Arrow
d(138424) = (3 + 1)(3 + 1)(1 + 1)
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d(138424) = (4)(4)(2)
Down Arrow
d(138424) = 32

More numbers for you to try

Take a look at the factors page to see the factors of 138,424 and how to find them.

Try the factor calculator.

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