Q: What is the total or count of factors of the number 204,243,100?

 A: 72

How do I find the total factors of the number 204,243,100?

Step 1

Find the prime factorization of the number 204,243,100.

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

Factor Tree
204,243,100
Factor Arrows
2102,121,550
Factor Arrows
251,060,775
Factor Arrows
510,212,155
Factor Arrows
52,042,431
Factor Arrows
17120,143
Factor Arrows
317379

The prime factorization in exponential form is: 22 x 52 x 171 x 3171 x 3791

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.

204,243,100 = 22 x 52 x 171 x 3171 x 3791
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d(n) = (a + 1)(b + 1)(c + 1)(d + 1)(e + 1)
Down Arrow
d(204243100) = (2 + 1)(2 + 1)(1 + 1)(1 + 1)(1 + 1)
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d(204243100) = (3)(3)(2)(2)(2)
Down Arrow
d(204243100) = 72

More numbers for you to try

Take a look at the factors page to see the factors of 204,243,100 and how to find them.

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