Q: What is the total or count of factors of the number 232,322,112?

 A: 168

How do I find the total factors of the number 232,322,112?

Step 1

Find the prime factorization of the number 232,322,112.

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

Factor Tree
232,322,112
Factor Arrows
2116,161,056
Factor Arrows
258,080,528
Factor Arrows
229,040,264
Factor Arrows
214,520,132
Factor Arrows
27,260,066
Factor Arrows
23,630,033
Factor Arrows
31,210,011
Factor Arrows
3403,337
Factor Arrows
1136,667
Factor Arrows
37991

The prime factorization in exponential form is: 26 x 32 x 111 x 371 x 9911

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.

232,322,112 = 26 x 32 x 111 x 371 x 9911
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)(d + 1)(e + 1)
Down Arrow
d(232322112) = (6 + 1)(2 + 1)(1 + 1)(1 + 1)(1 + 1)
Down Arrow
d(232322112) = (7)(3)(2)(2)(2)
Down Arrow
d(232322112) = 168

More numbers for you to try

Take a look at the factors page to see the factors of 232,322,112 and how to find them.

Try the factor calculator.

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