What is the Greatest Common Factor of 657 and 667?

Greatest common factor (GCF) of 657 and 667 is 1.

GCF(657,667) = 1

We will now calculate the prime factors of 657 and 667, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 657 and 667.

How to find the GCF of 657 and 667?

We will first find the prime factorization of 657 and 667. After we will calculate the factors of 657 and 667 and find the biggest common factor number .

Step-1: Prime Factorization of 657

Prime factors of 657 are 3, 73. Prime factorization of 657 in exponential form is:

657 = 3² × 73¹

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 657

List of positive integer factors of 657 that divides 657 without a remainder.

1, 3, 9, 73, 219

Step-4: Factors of 667

List of positive integer factors of 667 that divides 657 without a remainder.

1, 23, 29

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 657 and 667. The biggest common factor number is the GCF number.
So the greatest common factor 657 and 667 is 1.

Also check out the Least Common Multiple of 657 and 667