Q: What is the total or count of factors of the number 424,384?

 A: 28

How do I find the total factors of the number 424,384?

Step 1

Find the prime factorization of the number 424,384.

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

Factor Tree
424,384
Factor Arrows
2212,192
Factor Arrows
2106,096
Factor Arrows
253,048
Factor Arrows
226,524
Factor Arrows
213,262
Factor Arrows
26,631
Factor Arrows
19349

The prime factorization in exponential form is: 26 x 191 x 3491

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.

424,384 = 26 x 191 x 3491
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)
Down Arrow
d(424384) = (6 + 1)(1 + 1)(1 + 1)
Down Arrow
d(424384) = (7)(2)(2)
Down Arrow
d(424384) = 28

More numbers for you to try

Take a look at the factors page to see the factors of 424,384 and how to find them.

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