What is the Greatest Common Factor of 27306 and 27314?

Greatest common factor (GCF) of 27306 and 27314 is 2.

GCF(27306,27314) = 2

We will now calculate the prime factors of 27306 and 27314, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 27306 and 27314.

How to find the GCF of 27306 and 27314?

We will first find the prime factorization of 27306 and 27314. After we will calculate the factors of 27306 and 27314 and find the biggest common factor number .

Step-1: Prime Factorization of 27306

Prime factors of 27306 are 2, 3, 37, 41. Prime factorization of 27306 in exponential form is:

27306 = 2¹ × 3² × 37¹ × 41¹

Step-2: Prime Factorization of 27314

Prime factors of 27314 are 2, 7, 1951. Prime factorization of 27314 in exponential form is:

27314 = 2¹ × 7¹ × 1951¹

Step-3: Factors of 27306

List of positive integer factors of 27306 that divides 27306 without a remainder.

1, 2, 3, 6, 9, 18, 37, 41, 74, 82, 111, 123, 222, 246, 333, 369, 666, 738, 1517, 3034, 4551, 9102, 13653

Step-4: Factors of 27314

List of positive integer factors of 27314 that divides 27306 without a remainder.

1, 2, 7, 14, 1951, 3902, 13657

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 27306 and 27314. The biggest common factor number is the GCF number.
So the greatest common factor 27306 and 27314 is 2.

Also check out the Least Common Multiple of 27306 and 27314