Q: What is the total or count of factors of the number 2,209,116?

 A: 108

How do I find the total factors of the number 2,209,116?

Step 1

Find the prime factorization of the number 2,209,116.

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

Factor Tree
2,209,116
Factor Arrows
21,104,558
Factor Arrows
2552,279
Factor Arrows
3184,093
Factor Arrows
726,299
Factor Arrows
73,757
Factor Arrows
13289
Factor Arrows
1717

The prime factorization in exponential form is: 22 x 31 x 72 x 131 x 172

Step 2

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

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

2,209,116 = 22 x 31 x 72 x 131 x 172
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)(d + 1)(e + 1)
Down Arrow
d(2209116) = (2 + 1)(1 + 1)(2 + 1)(1 + 1)(2 + 1)
Down Arrow
d(2209116) = (3)(2)(3)(2)(3)
Down Arrow
d(2209116) = 108

More numbers for you to try

Take a look at the factors page to see the factors of 2,209,116 and how to find them.

Try the factor calculator.

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