Q: What is the total or count of factors of the number 120,384?

 A: 84

How do I find the total factors of the number 120,384?

Step 1

Find the prime factorization of the number 120,384.

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

Factor Tree
120,384
Factor Arrows
260,192
Factor Arrows
230,096
Factor Arrows
215,048
Factor Arrows
27,524
Factor Arrows
23,762
Factor Arrows
21,881
Factor Arrows
3627
Factor Arrows
3209
Factor Arrows
1119

The prime factorization in exponential form is: 26 x 32 x 111 x 191

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.

120,384 = 26 x 32 x 111 x 191
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)(d + 1)
Down Arrow
d(120384) = (6 + 1)(2 + 1)(1 + 1)(1 + 1)
Down Arrow
d(120384) = (7)(3)(2)(2)
Down Arrow
d(120384) = 84

More numbers for you to try

Take a look at the factors page to see the factors of 120,384 and how to find them.

Try the factor calculator.

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