Q: What is the total or count of factors of the number 237,166,120?

 A: 64

How do I find the total factors of the number 237,166,120?

Step 1

Find the prime factorization of the number 237,166,120.

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

Factor Tree
237,166,120
Factor Arrows
2118,583,060
Factor Arrows
259,291,530
Factor Arrows
229,645,765
Factor Arrows
55,929,153
Factor Arrows
31191,263
Factor Arrows
193991

The prime factorization in exponential form is: 23 x 51 x 311 x 1931 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.

237,166,120 = 23 x 51 x 311 x 1931 x 9911
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)(d + 1)(e + 1)
Down Arrow
d(237166120) = (3 + 1)(1 + 1)(1 + 1)(1 + 1)(1 + 1)
Down Arrow
d(237166120) = (4)(2)(2)(2)(2)
Down Arrow
d(237166120) = 64

More numbers for you to try

Take a look at the factors page to see the factors of 237,166,120 and how to find them.

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