What is the Greatest Common Factor of 27096 and 27114?

Greatest common factor (GCF) of 27096 and 27114 is 6.

GCF(27096,27114) = 6

We will now calculate the prime factors of 27096 and 27114, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 27096 and 27114.

How to find the GCF of 27096 and 27114?

We will first find the prime factorization of 27096 and 27114. After we will calculate the factors of 27096 and 27114 and find the biggest common factor number .

Step-1: Prime Factorization of 27096

Prime factors of 27096 are 2, 3, 1129. Prime factorization of 27096 in exponential form is:

27096 = 2³ × 3¹ × 1129¹

Step-2: Prime Factorization of 27114

Prime factors of 27114 are 2, 3, 4519. Prime factorization of 27114 in exponential form is:

27114 = 2¹ × 3¹ × 4519¹

Step-3: Factors of 27096

List of positive integer factors of 27096 that divides 27096 without a remainder.

1, 2, 3, 4, 6, 8, 12, 24, 1129, 2258, 3387, 4516, 6774, 9032, 13548

Step-4: Factors of 27114

List of positive integer factors of 27114 that divides 27096 without a remainder.

1, 2, 3, 6, 4519, 9038, 13557

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 27096 and 27114. The biggest common factor number is the GCF number.
So the greatest common factor 27096 and 27114 is 6.

Also check out the Least Common Multiple of 27096 and 27114