What is the Greatest Common Factor of 27710 and 27728?

Greatest common factor (GCF) of 27710 and 27728 is 2.

GCF(27710,27728) = 2

We will now calculate the prime factors of 27710 and 27728, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 27710 and 27728.

How to find the GCF of 27710 and 27728?

We will first find the prime factorization of 27710 and 27728. After we will calculate the factors of 27710 and 27728 and find the biggest common factor number .

Step-1: Prime Factorization of 27710

Prime factors of 27710 are 2, 5, 17, 163. Prime factorization of 27710 in exponential form is:

27710 = 2¹ × 5¹ × 17¹ × 163¹

Step-2: Prime Factorization of 27728

Prime factors of 27728 are 2, 1733. Prime factorization of 27728 in exponential form is:

27728 = 2⁴ × 1733¹

Step-3: Factors of 27710

List of positive integer factors of 27710 that divides 27710 without a remainder.

1, 2, 5, 10, 17, 34, 85, 163, 170, 326, 815, 1630, 2771, 5542, 13855

Step-4: Factors of 27728

List of positive integer factors of 27728 that divides 27710 without a remainder.

1, 2, 4, 8, 16, 1733, 3466, 6932, 13864

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 27710 and 27728. The biggest common factor number is the GCF number.
So the greatest common factor 27710 and 27728 is 2.

Also check out the Least Common Multiple of 27710 and 27728