Q: What is the total or count of factors of the number 110,208?

 A: 64

How do I find the total factors of the number 110,208?

Step 1

Find the prime factorization of the number 110,208.

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

Factor Tree
110,208
Factor Arrows
255,104
Factor Arrows
227,552
Factor Arrows
213,776
Factor Arrows
26,888
Factor Arrows
23,444
Factor Arrows
21,722
Factor Arrows
2861
Factor Arrows
3287
Factor Arrows
741

The prime factorization in exponential form is: 27 x 31 x 71 x 411

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.

110,208 = 27 x 31 x 71 x 411
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)(d + 1)
Down Arrow
d(110208) = (7 + 1)(1 + 1)(1 + 1)(1 + 1)
Down Arrow
d(110208) = (8)(2)(2)(2)
Down Arrow
d(110208) = 64

More numbers for you to try

Take a look at the factors page to see the factors of 110,208 and how to find them.

Try the factor calculator.

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