Q: What is the total or count of factors of the number 230,115,600?

 A: 480

How do I find the total factors of the number 230,115,600?

Step 1

Find the prime factorization of the number 230,115,600.

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

Factor Tree
230,115,600
Factor Arrows
2115,057,800
Factor Arrows
257,528,900
Factor Arrows
228,764,450
Factor Arrows
214,382,225
Factor Arrows
34,794,075
Factor Arrows
31,598,025
Factor Arrows
3532,675
Factor Arrows
5106,535
Factor Arrows
521,307
Factor Arrows
111,937
Factor Arrows
13149

The prime factorization in exponential form is: 24 x 33 x 52 x 111 x 131 x 1491

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.

230,115,600 = 24 x 33 x 52 x 111 x 131 x 1491
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)(d + 1)(e + 1)(f + 1)
Down Arrow
d(230115600) = (4 + 1)(3 + 1)(2 + 1)(1 + 1)(1 + 1)(1 + 1)
Down Arrow
d(230115600) = (5)(4)(3)(2)(2)(2)
Down Arrow
d(230115600) = 480

More numbers for you to try

Take a look at the factors page to see the factors of 230,115,600 and how to find them.

Try the factor calculator.

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