What is the Greatest Common Factor of 654 and 666?

Greatest common factor (GCF) of 654 and 666 is 6.

GCF(654,666) = 6

We will now calculate the prime factors of 654 and 666, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 654 and 666.

How to find the GCF of 654 and 666?

We will first find the prime factorization of 654 and 666. After we will calculate the factors of 654 and 666 and find the biggest common factor number .

Step-1: Prime Factorization of 654

Prime factors of 654 are 2, 3, 109. Prime factorization of 654 in exponential form is:

654 = 2¹ × 3¹ × 109¹

Step-2: Prime Factorization of 666

Prime factors of 666 are 2, 3, 37. Prime factorization of 666 in exponential form is:

666 = 2¹ × 3² × 37¹

Step-3: Factors of 654

List of positive integer factors of 654 that divides 654 without a remainder.

1, 2, 3, 6, 109, 218, 327

Step-4: Factors of 666

List of positive integer factors of 666 that divides 654 without a remainder.

1, 2, 3, 6, 9, 18, 37, 74, 111, 222, 333

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 654 and 666. The biggest common factor number is the GCF number.
So the greatest common factor 654 and 666 is 6.

Also check out the Least Common Multiple of 654 and 666