Q: What is the total or count of factors of the number 3,456?

 A: 32

How do I find the total factors of the number 3,456?

Step 1

Find the prime factorization of the number 3,456.

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

Factor Tree
3,456
Factor Arrows
21,728
Factor Arrows
2864
Factor Arrows
2432
Factor Arrows
2216
Factor Arrows
2108
Factor Arrows
254
Factor Arrows
227
Factor Arrows
39
Factor Arrows
33

The prime factorization in exponential form is: 27 x 33

Step 2

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

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

3,456 = 27 x 33
Down Arrow
d(n) = (a + 1)(b + 1)
Down Arrow
d(3456) = (7 + 1)(3 + 1)
Down Arrow
d(3456) = (8)(4)
Down Arrow
d(3456) = 32

More numbers for you to try

Take a look at the factors page to see the factors of 3,456 and how to find them.

Try the factor calculator.

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