Q: What is the total or count of factors of the number 57,288?

 A: 64

How do I find the total factors of the number 57,288?

Step 1

Find the prime factorization of the number 57,288.

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

Factor Tree
57,288
Factor Arrows
228,644
Factor Arrows
214,322
Factor Arrows
27,161
Factor Arrows
32,387
Factor Arrows
7341
Factor Arrows
1131

The prime factorization in exponential form is: 23 x 31 x 71 x 111 x 311

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.

57,288 = 23 x 31 x 71 x 111 x 311
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)(d + 1)(e + 1)
Down Arrow
d(57288) = (3 + 1)(1 + 1)(1 + 1)(1 + 1)(1 + 1)
Down Arrow
d(57288) = (4)(2)(2)(2)(2)
Down Arrow
d(57288) = 64

More numbers for you to try

Take a look at the factors page to see the factors of 57,288 and how to find them.

Try the factor calculator.

Explore more about the number 57,288:


Ask a Question