Q: What is the total or count of factors of the number 110,011,000?

 A: 128

How do I find the total factors of the number 110,011,000?

Step 1

Find the prime factorization of the number 110,011,000.

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

Factor Tree
110,011,000
Factor Arrows
255,005,500
Factor Arrows
227,502,750
Factor Arrows
213,751,375
Factor Arrows
52,750,275
Factor Arrows
5550,055
Factor Arrows
5110,011
Factor Arrows
1110,001
Factor Arrows
73137

The prime factorization in exponential form is: 23 x 53 x 111 x 731 x 1371

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.

110,011,000 = 23 x 53 x 111 x 731 x 1371
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)(d + 1)(e + 1)
Down Arrow
d(110011000) = (3 + 1)(3 + 1)(1 + 1)(1 + 1)(1 + 1)
Down Arrow
d(110011000) = (4)(4)(2)(2)(2)
Down Arrow
d(110011000) = 128

More numbers for you to try

Take a look at the factors page to see the factors of 110,011,000 and how to find them.

Try the factor calculator.

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