Q: What is the total or count of factors of the number 102,243,096?

 A: 96

How do I find the total factors of the number 102,243,096?

Step 1

Find the prime factorization of the number 102,243,096.

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

Factor Tree
102,243,096
Factor Arrows
251,121,548
Factor Arrows
225,560,774
Factor Arrows
212,780,387
Factor Arrows
34,260,129
Factor Arrows
31,420,043
Factor Arrows
2361,741
Factor Arrows
292,129

The prime factorization in exponential form is: 23 x 32 x 231 x 291 x 2,1291

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.

102,243,096 = 23 x 32 x 231 x 291 x 2,1291
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d(n) = (a + 1)(b + 1)(c + 1)(d + 1)(e + 1)
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d(102243096) = (3 + 1)(2 + 1)(1 + 1)(1 + 1)(1 + 1)
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d(102243096) = (4)(3)(2)(2)(2)
Down Arrow
d(102243096) = 96

More numbers for you to try

Take a look at the factors page to see the factors of 102,243,096 and how to find them.

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