Q: What is the total or count of factors of the number 3,564,288?

 A: 216

How do I find the total factors of the number 3,564,288?

Step 1

Find the prime factorization of the number 3,564,288.

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

Factor Tree
3,564,288
Factor Arrows
21,782,144
Factor Arrows
2891,072
Factor Arrows
2445,536
Factor Arrows
2222,768
Factor Arrows
2111,384
Factor Arrows
255,692
Factor Arrows
227,846
Factor Arrows
213,923
Factor Arrows
34,641
Factor Arrows
31,547
Factor Arrows
7221
Factor Arrows
1317

The prime factorization in exponential form is: 28 x 32 x 71 x 131 x 171

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.

3,564,288 = 28 x 32 x 71 x 131 x 171
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)(d + 1)(e + 1)
Down Arrow
d(3564288) = (8 + 1)(2 + 1)(1 + 1)(1 + 1)(1 + 1)
Down Arrow
d(3564288) = (9)(3)(2)(2)(2)
Down Arrow
d(3564288) = 216

More numbers for you to try

Take a look at the factors page to see the factors of 3,564,288 and how to find them.

Try the factor calculator.

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