What is the Greatest Common Factor of 27114 and 27132?

Greatest common factor (GCF) of 27114 and 27132 is 6.

GCF(27114,27132) = 6

We will now calculate the prime factors of 27114 and 27132, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 27114 and 27132.

How to find the GCF of 27114 and 27132?

We will first find the prime factorization of 27114 and 27132. After we will calculate the factors of 27114 and 27132 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 27132

Prime factors of 27132 are 2, 3, 7, 17, 19. Prime factorization of 27132 in exponential form is:

27132 = 2² × 3¹ × 7¹ × 17¹ × 19¹

Step-3: Factors of 27114

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

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

Step-4: Factors of 27132

List of positive integer factors of 27132 that divides 27114 without a remainder.

1, 2, 3, 4, 6, 7, 12, 14, 17, 19, 21, 28, 34, 38, 42, 51, 57, 68, 76, 84, 102, 114, 119, 133, 204, 228, 238, 266, 323, 357, 399, 476, 532, 646, 714, 798, 969, 1292, 1428, 1596, 1938, 2261, 3876, 4522, 6783, 9044, 13566

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 27114 and 27132. The biggest common factor number is the GCF number.
So the greatest common factor 27114 and 27132 is 6.

Also check out the Least Common Multiple of 27114 and 27132