What is the Greatest Common Factor of 6720 and 6738?

Greatest common factor (GCF) of 6720 and 6738 is 6.

GCF(6720,6738) = 6

We will now calculate the prime factors of 6720 and 6738, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 6720 and 6738.

How to find the GCF of 6720 and 6738?

We will first find the prime factorization of 6720 and 6738. After we will calculate the factors of 6720 and 6738 and find the biggest common factor number .

Step-1: Prime Factorization of 6720

Prime factors of 6720 are 2, 3, 5, 7. Prime factorization of 6720 in exponential form is:

6720 = 2⁶ × 3¹ × 5¹ × 7¹

Step-2: Prime Factorization of 6738

Prime factors of 6738 are 2, 3, 1123. Prime factorization of 6738 in exponential form is:

6738 = 2¹ × 3¹ × 1123¹

Step-3: Factors of 6720

List of positive integer factors of 6720 that divides 6720 without a remainder.

1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 16, 20, 21, 24, 28, 30, 32, 35, 40, 42, 48, 56, 60, 64, 70, 80, 84, 96, 105, 112, 120, 140, 160, 168, 192, 210, 224, 240, 280, 320, 336, 420, 448, 480, 560, 672, 840, 960, 1120, 1344, 1680, 2240, 3360

Step-4: Factors of 6738

List of positive integer factors of 6738 that divides 6720 without a remainder.

1, 2, 3, 6, 1123, 2246, 3369

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 6720 and 6738. The biggest common factor number is the GCF number.
So the greatest common factor 6720 and 6738 is 6.

Also check out the Least Common Multiple of 6720 and 6738