What is the Greatest Common Factor of 684 and 696?

Greatest common factor (GCF) of 684 and 696 is 12.

GCF(684,696) = 12

We will now calculate the prime factors of 684 and 696, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 684 and 696.

How to find the GCF of 684 and 696?

We will first find the prime factorization of 684 and 696. After we will calculate the factors of 684 and 696 and find the biggest common factor number .

Step-1: Prime Factorization of 684

Prime factors of 684 are 2, 3, 19. Prime factorization of 684 in exponential form is:

684 = 2² × 3² × 19¹

Step-2: Prime Factorization of 696

Prime factors of 696 are 2, 3, 29. Prime factorization of 696 in exponential form is:

696 = 2³ × 3¹ × 29¹

Step-3: Factors of 684

List of positive integer factors of 684 that divides 684 without a remainder.

1, 2, 3, 4, 6, 9, 12, 18, 19, 36, 38, 57, 76, 114, 171, 228, 342

Step-4: Factors of 696

List of positive integer factors of 696 that divides 684 without a remainder.

1, 2, 3, 4, 6, 8, 12, 24, 29, 58, 87, 116, 174, 232, 348

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 684 and 696. The biggest common factor number is the GCF number.
So the greatest common factor 684 and 696 is 12.

Also check out the Least Common Multiple of 684 and 696