Q: What is the total or count of factors of the number 242,110,328?

 A: 96

How do I find the total factors of the number 242,110,328?

Step 1

Find the prime factorization of the number 242,110,328.

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

Factor Tree
242,110,328
Factor Arrows
2121,055,164
Factor Arrows
260,527,582
Factor Arrows
230,263,791
Factor Arrows
171,780,223
Factor Arrows
17104,719
Factor Arrows
234,553
Factor Arrows
29157

The prime factorization in exponential form is: 23 x 172 x 231 x 291 x 1571

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.

242,110,328 = 23 x 172 x 231 x 291 x 1571
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)(d + 1)(e + 1)
Down Arrow
d(242110328) = (3 + 1)(2 + 1)(1 + 1)(1 + 1)(1 + 1)
Down Arrow
d(242110328) = (4)(3)(2)(2)(2)
Down Arrow
d(242110328) = 96

More numbers for you to try

Take a look at the factors page to see the factors of 242,110,328 and how to find them.

Try the factor calculator.

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