Q: What is the total or count of factors of the number 110,606,100?

 A: 144

How do I find the total factors of the number 110,606,100?

Step 1

Find the prime factorization of the number 110,606,100.

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

Factor Tree
110,606,100
Factor Arrows
255,303,050
Factor Arrows
227,651,525
Factor Arrows
39,217,175
Factor Arrows
51,843,435
Factor Arrows
5368,687
Factor Arrows
1133,517
Factor Arrows
113,047
Factor Arrows
11277

The prime factorization in exponential form is: 22 x 31 x 52 x 113 x 2771

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)(e + 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.

110,606,100 = 22 x 31 x 52 x 113 x 2771
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)(d + 1)(e + 1)
Down Arrow
d(110606100) = (2 + 1)(1 + 1)(2 + 1)(3 + 1)(1 + 1)
Down Arrow
d(110606100) = (3)(2)(3)(4)(2)
Down Arrow
d(110606100) = 144

More numbers for you to try

Take a look at the factors page to see the factors of 110,606,100 and how to find them.

Try the factor calculator.

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