Q: What is the total or count of factors of the number 22,167,216?

 A: 120

How do I find the total factors of the number 22,167,216?

Step 1

Find the prime factorization of the number 22,167,216.

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

Factor Tree
22,167,216
Factor Arrows
211,083,608
Factor Arrows
25,541,804
Factor Arrows
22,770,902
Factor Arrows
21,385,451
Factor Arrows
3461,817
Factor Arrows
3153,939
Factor Arrows
351,313
Factor Arrows
232,231
Factor Arrows
2397

The prime factorization in exponential form is: 24 x 33 x 232 x 971

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)

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.

22,167,216 = 24 x 33 x 232 x 971
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)(d + 1)
Down Arrow
d(22167216) = (4 + 1)(3 + 1)(2 + 1)(1 + 1)
Down Arrow
d(22167216) = (5)(4)(3)(2)
Down Arrow
d(22167216) = 120

More numbers for you to try

Take a look at the factors page to see the factors of 22,167,216 and how to find them.

Try the factor calculator.

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