Q: What is the total or count of factors of the number 228,412,000?

 A: 96

How do I find the total factors of the number 228,412,000?

Step 1

Find the prime factorization of the number 228,412,000.

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

Factor Tree
228,412,000
Factor Arrows
2114,206,000
Factor Arrows
257,103,000
Factor Arrows
228,551,500
Factor Arrows
214,275,750
Factor Arrows
27,137,875
Factor Arrows
51,427,575
Factor Arrows
5285,515
Factor Arrows
557,103
Factor Arrows
173,359

The prime factorization in exponential form is: 25 x 53 x 171 x 3,3591

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)

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.

228,412,000 = 25 x 53 x 171 x 3,3591
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)(d + 1)
Down Arrow
d(228412000) = (5 + 1)(3 + 1)(1 + 1)(1 + 1)
Down Arrow
d(228412000) = (6)(4)(2)(2)
Down Arrow
d(228412000) = 96

More numbers for you to try

Take a look at the factors page to see the factors of 228,412,000 and how to find them.

Try the factor calculator.

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