What is the Greatest Common Factor of 657 and 663?

Greatest common factor (GCF) of 657 and 663 is 3.

GCF(657,663) = 3

We will now calculate the prime factors of 657 and 663, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 657 and 663.

How to find the GCF of 657 and 663?

We will first find the prime factorization of 657 and 663. After we will calculate the factors of 657 and 663 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 663

Prime factors of 663 are 3, 13, 17. Prime factorization of 663 in exponential form is:

663 = 3¹ × 13¹ × 17¹

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 663

List of positive integer factors of 663 that divides 657 without a remainder.

1, 3, 13, 17, 39, 51, 221

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 657 and 663. The biggest common factor number is the GCF number.
So the greatest common factor 657 and 663 is 3.

Also check out the Least Common Multiple of 657 and 663