Q: What is the total or count of factors of the number 30,456?

 A: 40

How do I find the total factors of the number 30,456?

Step 1

Find the prime factorization of the number 30,456.

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

Factor Tree
30,456
Factor Arrows
215,228
Factor Arrows
27,614
Factor Arrows
23,807
Factor Arrows
31,269
Factor Arrows
3423
Factor Arrows
3141
Factor Arrows
347

The prime factorization in exponential form is: 23 x 34 x 471

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.

30,456 = 23 x 34 x 471
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)
Down Arrow
d(30456) = (3 + 1)(4 + 1)(1 + 1)
Down Arrow
d(30456) = (4)(5)(2)
Down Arrow
d(30456) = 40

More numbers for you to try

Take a look at the factors page to see the factors of 30,456 and how to find them.

Try the factor calculator.

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