What is the Greatest Common Factor of 684 and 704?

Greatest common factor (GCF) of 684 and 704 is 4.

GCF(684,704) = 4

We will now calculate the prime factors of 684 and 704, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 684 and 704.

How to find the GCF of 684 and 704?

We will first find the prime factorization of 684 and 704. After we will calculate the factors of 684 and 704 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 704

Prime factors of 704 are 2, 11. Prime factorization of 704 in exponential form is:

704 = 2⁶ × 11¹

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 704

List of positive integer factors of 704 that divides 684 without a remainder.

1, 2, 4, 8, 11, 16, 22, 32, 44, 64, 88, 176, 352

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 684 and 704. The biggest common factor number is the GCF number.
So the greatest common factor 684 and 704 is 4.

Also check out the Least Common Multiple of 684 and 704