Q: What is the total or count of factors of the number 282,372,800?

 A: 84

How do I find the total factors of the number 282,372,800?

Step 1

Find the prime factorization of the number 282,372,800.

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

Factor Tree
282,372,800
Factor Arrows
2141,186,400
Factor Arrows
270,593,200
Factor Arrows
235,296,600
Factor Arrows
217,648,300
Factor Arrows
28,824,150
Factor Arrows
24,412,075
Factor Arrows
5882,415
Factor Arrows
5176,483
Factor Arrows
315,693

The prime factorization in exponential form is: 26 x 52 x 311 x 5,6931

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.

282,372,800 = 26 x 52 x 311 x 5,6931
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)(d + 1)
Down Arrow
d(282372800) = (6 + 1)(2 + 1)(1 + 1)(1 + 1)
Down Arrow
d(282372800) = (7)(3)(2)(2)
Down Arrow
d(282372800) = 84

More numbers for you to try

Take a look at the factors page to see the factors of 282,372,800 and how to find them.

Try the factor calculator.

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