Q: What is the total or count of factors of the number 314,304?

 A: 28

How do I find the total factors of the number 314,304?

Step 1

Find the prime factorization of the number 314,304.

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

Factor Tree
314,304
Factor Arrows
2157,152
Factor Arrows
278,576
Factor Arrows
239,288
Factor Arrows
219,644
Factor Arrows
29,822
Factor Arrows
24,911
Factor Arrows
31,637

The prime factorization in exponential form is: 26 x 31 x 1,6371

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.

314,304 = 26 x 31 x 1,6371
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)
Down Arrow
d(314304) = (6 + 1)(1 + 1)(1 + 1)
Down Arrow
d(314304) = (7)(2)(2)
Down Arrow
d(314304) = 28

More numbers for you to try

Take a look at the factors page to see the factors of 314,304 and how to find them.

Try the factor calculator.

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