Q: What is the total or count of factors of the number 242,414,144?

 A: 56

How do I find the total factors of the number 242,414,144?

Step 1

Find the prime factorization of the number 242,414,144.

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

Factor Tree
242,414,144
Factor Arrows
2121,207,072
Factor Arrows
260,603,536
Factor Arrows
230,301,768
Factor Arrows
215,150,884
Factor Arrows
27,575,442
Factor Arrows
23,787,721
Factor Arrows
7541,103
Factor Arrows
1912,833

The prime factorization in exponential form is: 26 x 71 x 1911 x 2,8331

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.

242,414,144 = 26 x 71 x 1911 x 2,8331
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)(d + 1)
Down Arrow
d(242414144) = (6 + 1)(1 + 1)(1 + 1)(1 + 1)
Down Arrow
d(242414144) = (7)(2)(2)(2)
Down Arrow
d(242414144) = 56

More numbers for you to try

Take a look at the factors page to see the factors of 242,414,144 and how to find them.

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