What is the Greatest Common Factor of 684 and 700?

Greatest common factor (GCF) of 684 and 700 is 4.

GCF(684,700) = 4

We will now calculate the prime factors of 684 and 700, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 684 and 700.

How to find the GCF of 684 and 700?

We will first find the prime factorization of 684 and 700. After we will calculate the factors of 684 and 700 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 700

Prime factors of 700 are 2, 5, 7. Prime factorization of 700 in exponential form is:

700 = 2² × 5² × 7¹

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 700

List of positive integer factors of 700 that divides 684 without a remainder.

1, 2, 4, 5, 7, 10, 14, 20, 25, 28, 35, 50, 70, 100, 140, 175, 350

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 684 and 700. The biggest common factor number is the GCF number.
So the greatest common factor 684 and 700 is 4.

Also check out the Least Common Multiple of 684 and 700