Q: What is the total or count of factors of the number 384,192?

 A: 84

How do I find the total factors of the number 384,192?

Step 1

Find the prime factorization of the number 384,192.

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

Factor Tree
384,192
Factor Arrows
2192,096
Factor Arrows
296,048
Factor Arrows
248,024
Factor Arrows
224,012
Factor Arrows
212,006
Factor Arrows
26,003
Factor Arrows
32,001
Factor Arrows
3667
Factor Arrows
2329

The prime factorization in exponential form is: 26 x 32 x 231 x 291

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.

384,192 = 26 x 32 x 231 x 291
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)(d + 1)
Down Arrow
d(384192) = (6 + 1)(2 + 1)(1 + 1)(1 + 1)
Down Arrow
d(384192) = (7)(3)(2)(2)
Down Arrow
d(384192) = 84

More numbers for you to try

Take a look at the factors page to see the factors of 384,192 and how to find them.

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