What is the Greatest Common Factor of 654 and 667?

Greatest common factor (GCF) of 654 and 667 is 1.

GCF(654,667) = 1

We will now calculate the prime factors of 654 and 667, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 654 and 667.

How to find the GCF of 654 and 667?

We will first find the prime factorization of 654 and 667. After we will calculate the factors of 654 and 667 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 667

Prime factors of 667 are 23, 29. Prime factorization of 667 in exponential form is:

667 = 23¹ × 29¹

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 667

List of positive integer factors of 667 that divides 654 without a remainder.

1, 23, 29

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 654 and 667. The biggest common factor number is the GCF number.
So the greatest common factor 654 and 667 is 1.

Also check out the Least Common Multiple of 654 and 667