Q: What is the total or count of factors of the number 120,120,300?

 A: 144

How do I find the total factors of the number 120,120,300?

Step 1

Find the prime factorization of the number 120,120,300.

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

Factor Tree
120,120,300
Factor Arrows
260,060,150
Factor Arrows
230,030,075
Factor Arrows
310,010,025
Factor Arrows
33,336,675
Factor Arrows
31,112,225
Factor Arrows
5222,445
Factor Arrows
544,489
Factor Arrows
172,617

The prime factorization in exponential form is: 22 x 33 x 52 x 171 x 2,6171

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.

120,120,300 = 22 x 33 x 52 x 171 x 2,6171
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)(d + 1)(e + 1)
Down Arrow
d(120120300) = (2 + 1)(3 + 1)(2 + 1)(1 + 1)(1 + 1)
Down Arrow
d(120120300) = (3)(4)(3)(2)(2)
Down Arrow
d(120120300) = 144

More numbers for you to try

Take a look at the factors page to see the factors of 120,120,300 and how to find them.

Try the factor calculator.

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