What is the Greatest Common Factor of 54 and 66?

Greatest common factor (GCF) of 54 and 66 is 6.

GCF(54,66) = 6

We will now calculate the prime factors of 54 and 66, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 54 and 66.

How to find the GCF of 54 and 66?

We will first find the prime factorization of 54 and 66. After we will calculate the factors of 54 and 66 and find the biggest common factor number .

Step-1: Prime Factorization of 54

Prime factors of 54 are 2, 3. Prime factorization of 54 in exponential form is:

54 = 2¹ × 3³

Step-2: Prime Factorization of 66

Prime factors of 66 are 2, 3, 11. Prime factorization of 66 in exponential form is:

66 = 2¹ × 3¹ × 11¹

Step-3: Factors of 54

List of positive integer factors of 54 that divides 54 without a remainder.

1, 2, 3, 6, 9, 18, 27

Step-4: Factors of 66

List of positive integer factors of 66 that divides 54 without a remainder.

1, 2, 3, 6, 11, 22, 33

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 54 and 66. The biggest common factor number is the GCF number.
So the greatest common factor 54 and 66 is 6.

Also check out the Least Common Multiple of 54 and 66