Q: What is the total or count of factors of the number 230,573,448?

 A: 144

How do I find the total factors of the number 230,573,448?

Step 1

Find the prime factorization of the number 230,573,448.

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

Factor Tree
230,573,448
Factor Arrows
2115,286,724
Factor Arrows
257,643,362
Factor Arrows
228,821,681
Factor Arrows
39,607,227
Factor Arrows
33,202,409
Factor Arrows
7457,487
Factor Arrows
1726,911
Factor Arrows
171,583

The prime factorization in exponential form is: 23 x 32 x 71 x 172 x 1,5831

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.

230,573,448 = 23 x 32 x 71 x 172 x 1,5831
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)(d + 1)(e + 1)
Down Arrow
d(230573448) = (3 + 1)(2 + 1)(1 + 1)(2 + 1)(1 + 1)
Down Arrow
d(230573448) = (4)(3)(2)(3)(2)
Down Arrow
d(230573448) = 144

More numbers for you to try

Take a look at the factors page to see the factors of 230,573,448 and how to find them.

Try the factor calculator.

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