Q: What is the total or count of factors of the number 33,696?

 A: 60

How do I find the total factors of the number 33,696?

Step 1

Find the prime factorization of the number 33,696.

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

Factor Tree
33,696
Factor Arrows
216,848
Factor Arrows
28,424
Factor Arrows
24,212
Factor Arrows
22,106
Factor Arrows
21,053
Factor Arrows
3351
Factor Arrows
3117
Factor Arrows
339
Factor Arrows
313

The prime factorization in exponential form is: 25 x 34 x 131

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.

33,696 = 25 x 34 x 131
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)
Down Arrow
d(33696) = (5 + 1)(4 + 1)(1 + 1)
Down Arrow
d(33696) = (6)(5)(2)
Down Arrow
d(33696) = 60

More numbers for you to try

Take a look at the factors page to see the factors of 33,696 and how to find them.

Try the factor calculator.

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