Q: What is the total or count of factors of the number 26,112?

 A: 40

How do I find the total factors of the number 26,112?

Step 1

Find the prime factorization of the number 26,112.

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

Factor Tree
26,112
Factor Arrows
213,056
Factor Arrows
26,528
Factor Arrows
23,264
Factor Arrows
21,632
Factor Arrows
2816
Factor Arrows
2408
Factor Arrows
2204
Factor Arrows
2102
Factor Arrows
251
Factor Arrows
317

The prime factorization in exponential form is: 29 x 31 x 171

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.

26,112 = 29 x 31 x 171
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)
Down Arrow
d(26112) = (9 + 1)(1 + 1)(1 + 1)
Down Arrow
d(26112) = (10)(2)(2)
Down Arrow
d(26112) = 40

More numbers for you to try

Take a look at the factors page to see the factors of 26,112 and how to find them.

Try the factor calculator.

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