Q: What is the total or count of factors of the number 222,123,006?

 A: 128

How do I find the total factors of the number 222,123,006?

Step 1

Find the prime factorization of the number 222,123,006.

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

Factor Tree
222,123,006
Factor Arrows
2111,061,503
Factor Arrows
337,020,501
Factor Arrows
312,340,167
Factor Arrows
34,113,389
Factor Arrows
7587,627
Factor Arrows
2325,549
Factor Arrows
29881

The prime factorization in exponential form is: 21 x 33 x 71 x 231 x 291 x 8811

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)(f + 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.

222,123,006 = 21 x 33 x 71 x 231 x 291 x 8811
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d(n) = (a + 1)(b + 1)(c + 1)(d + 1)(e + 1)(f + 1)
Down Arrow
d(222123006) = (1 + 1)(3 + 1)(1 + 1)(1 + 1)(1 + 1)(1 + 1)
Down Arrow
d(222123006) = (2)(4)(2)(2)(2)(2)
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d(222123006) = 128

More numbers for you to try

Take a look at the factors page to see the factors of 222,123,006 and how to find them.

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