What is the Greatest Common Factor of 684 and 702?

Greatest common factor (GCF) of 684 and 702 is 18.

GCF(684,702) = 18

We will now calculate the prime factors of 684 and 702, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 684 and 702.

How to find the GCF of 684 and 702?

We will first find the prime factorization of 684 and 702. After we will calculate the factors of 684 and 702 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 702

Prime factors of 702 are 2, 3, 13. Prime factorization of 702 in exponential form is:

702 = 2¹ × 3³ × 13¹

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 702

List of positive integer factors of 702 that divides 684 without a remainder.

1, 2, 3, 6, 9, 13, 18, 26, 27, 39, 54, 78, 117, 234, 351

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 684 and 702. The biggest common factor number is the GCF number.
So the greatest common factor 684 and 702 is 18.

Also check out the Least Common Multiple of 684 and 702