What is the Greatest Common Factor of 27768 and 27774?

Greatest common factor (GCF) of 27768 and 27774 is 6.

GCF(27768,27774) = 6

We will now calculate the prime factors of 27768 and 27774, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 27768 and 27774.

How to find the GCF of 27768 and 27774?

We will first find the prime factorization of 27768 and 27774. After we will calculate the factors of 27768 and 27774 and find the biggest common factor number .

Step-1: Prime Factorization of 27768

Prime factors of 27768 are 2, 3, 13, 89. Prime factorization of 27768 in exponential form is:

27768 = 2³ × 3¹ × 13¹ × 89¹

Step-2: Prime Factorization of 27774

Prime factors of 27774 are 2, 3, 1543. Prime factorization of 27774 in exponential form is:

27774 = 2¹ × 3² × 1543¹

Step-3: Factors of 27768

List of positive integer factors of 27768 that divides 27768 without a remainder.

1, 2, 3, 4, 6, 8, 12, 13, 24, 26, 39, 52, 78, 89, 104, 156, 178, 267, 312, 356, 534, 712, 1068, 1157, 2136, 2314, 3471, 4628, 6942, 9256, 13884

Step-4: Factors of 27774

List of positive integer factors of 27774 that divides 27768 without a remainder.

1, 2, 3, 6, 9, 18, 1543, 3086, 4629, 9258, 13887

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 27768 and 27774. The biggest common factor number is the GCF number.
So the greatest common factor 27768 and 27774 is 6.

Also check out the Least Common Multiple of 27768 and 27774