What is the Greatest Common Factor of 684 and 690?

Greatest common factor (GCF) of 684 and 690 is 6.

GCF(684,690) = 6

We will now calculate the prime factors of 684 and 690, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 684 and 690.

How to find the GCF of 684 and 690?

We will first find the prime factorization of 684 and 690. After we will calculate the factors of 684 and 690 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 690

Prime factors of 690 are 2, 3, 5, 23. Prime factorization of 690 in exponential form is:

690 = 2¹ × 3¹ × 5¹ × 23¹

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 690

List of positive integer factors of 690 that divides 684 without a remainder.

1, 2, 3, 5, 6, 10, 15, 23, 30, 46, 69, 115, 138, 230, 345

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 684 and 690. The biggest common factor number is the GCF number.
So the greatest common factor 684 and 690 is 6.

Also check out the Least Common Multiple of 684 and 690