Q: What is the total or count of factors of the number 3,600?

 A: 45

How do I find the total factors of the number 3,600?

Step 1

Find the prime factorization of the number 3,600.

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

Factor Tree
3,600
Factor Arrows
21,800
Factor Arrows
2900
Factor Arrows
2450
Factor Arrows
2225
Factor Arrows
375
Factor Arrows
325
Factor Arrows
55

The prime factorization in exponential form is: 24 x 32 x 52

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.

3,600 = 24 x 32 x 52
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)
Down Arrow
d(3600) = (4 + 1)(2 + 1)(2 + 1)
Down Arrow
d(3600) = (5)(3)(3)
Down Arrow
d(3600) = 45

More numbers for you to try

Take a look at the factors page to see the factors of 3,600 and how to find them.

Try the factor calculator.

Explore more about the number 3,600:


Ask a Question