Q: What is the total or count of factors of the number 387,648?

 A: 42

How do I find the total factors of the number 387,648?

Step 1

Find the prime factorization of the number 387,648.

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

Factor Tree
387,648
Factor Arrows
2193,824
Factor Arrows
296,912
Factor Arrows
248,456
Factor Arrows
224,228
Factor Arrows
212,114
Factor Arrows
26,057
Factor Arrows
32,019
Factor Arrows
3673

The prime factorization in exponential form is: 26 x 32 x 6731

Step 2

Setup the equation for determining the number of factors or divisors. The equation is:

d(n) = (a + 1)(b + 1)(c + 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.

387,648 = 26 x 32 x 6731
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)
Down Arrow
d(387648) = (6 + 1)(2 + 1)(1 + 1)
Down Arrow
d(387648) = (7)(3)(2)
Down Arrow
d(387648) = 42

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Take a look at the factors page to see the factors of 387,648 and how to find them.

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