Q: What is the total or count of factors of the number 27,084,120?

 A: 128

How do I find the total factors of the number 27,084,120?

Step 1

Find the prime factorization of the number 27,084,120.

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

Factor Tree
27,084,120
Factor Arrows
213,542,060
Factor Arrows
26,771,030
Factor Arrows
23,385,515
Factor Arrows
31,128,505
Factor Arrows
5225,701
Factor Arrows
732,243
Factor Arrows
191,697

The prime factorization in exponential form is: 23 x 31 x 51 x 71 x 191 x 1,6971

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)(f + 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.

27,084,120 = 23 x 31 x 51 x 71 x 191 x 1,6971
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d(n) = (a + 1)(b + 1)(c + 1)(d + 1)(e + 1)(f + 1)
Down Arrow
d(27084120) = (3 + 1)(1 + 1)(1 + 1)(1 + 1)(1 + 1)(1 + 1)
Down Arrow
d(27084120) = (4)(2)(2)(2)(2)(2)
Down Arrow
d(27084120) = 128

More numbers for you to try

Take a look at the factors page to see the factors of 27,084,120 and how to find them.

Try the factor calculator.

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