What is the Greatest Common Factor of 663 and 678?

Greatest common factor (GCF) of 663 and 678 is 3.

GCF(663,678) = 3

We will now calculate the prime factors of 663 and 678, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 663 and 678.

How to find the GCF of 663 and 678?

We will first find the prime factorization of 663 and 678. After we will calculate the factors of 663 and 678 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 678

Prime factors of 678 are 2, 3, 113. Prime factorization of 678 in exponential form is:

678 = 2¹ × 3¹ × 113¹

Step-3: Factors of 663

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

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

Step-4: Factors of 678

List of positive integer factors of 678 that divides 663 without a remainder.

1, 2, 3, 6, 113, 226, 339

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 663 and 678. The biggest common factor number is the GCF number.
So the greatest common factor 663 and 678 is 3.

Also check out the Least Common Multiple of 663 and 678