Q: What is the total or count of factors of the number 27,375,712?

 A: 144

How do I find the total factors of the number 27,375,712?

Step 1

Find the prime factorization of the number 27,375,712.

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

Factor Tree
27,375,712
Factor Arrows
213,687,856
Factor Arrows
26,843,928
Factor Arrows
23,421,964
Factor Arrows
21,710,982
Factor Arrows
2855,491
Factor Arrows
7122,213
Factor Arrows
717,459
Factor Arrows
131,343
Factor Arrows
1779

The prime factorization in exponential form is: 25 x 72 x 131 x 171 x 791

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.

27,375,712 = 25 x 72 x 131 x 171 x 791
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)(d + 1)(e + 1)
Down Arrow
d(27375712) = (5 + 1)(2 + 1)(1 + 1)(1 + 1)(1 + 1)
Down Arrow
d(27375712) = (6)(3)(2)(2)(2)
Down Arrow
d(27375712) = 144

More numbers for you to try

Take a look at the factors page to see the factors of 27,375,712 and how to find them.

Try the factor calculator.

Explore more about the number 27,375,712:


Ask a Question