What is the Greatest Common Factor of 684 and 699?

Greatest common factor (GCF) of 684 and 699 is 3.

GCF(684,699) = 3

We will now calculate the prime factors of 684 and 699, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 684 and 699.

How to find the GCF of 684 and 699?

We will first find the prime factorization of 684 and 699. After we will calculate the factors of 684 and 699 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 699

Prime factors of 699 are 3, 233. Prime factorization of 699 in exponential form is:

699 = 3¹ × 233¹

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 699

List of positive integer factors of 699 that divides 684 without a remainder.

1, 3, 233

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 684 and 699. The biggest common factor number is the GCF number.
So the greatest common factor 684 and 699 is 3.

Also check out the Least Common Multiple of 684 and 699