What is the Greatest Common Factor of 6738 and 6756?

Greatest common factor (GCF) of 6738 and 6756 is 6.

GCF(6738,6756) = 6

We will now calculate the prime factors of 6738 and 6756, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 6738 and 6756.

How to find the GCF of 6738 and 6756?

We will first find the prime factorization of 6738 and 6756. After we will calculate the factors of 6738 and 6756 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 6756

Prime factors of 6756 are 2, 3, 563. Prime factorization of 6756 in exponential form is:

6756 = 2² × 3¹ × 563¹

Step-3: Factors of 6738

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

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

Step-4: Factors of 6756

List of positive integer factors of 6756 that divides 6738 without a remainder.

1, 2, 3, 4, 6, 12, 563, 1126, 1689, 2252, 3378

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 6738 and 6756. The biggest common factor number is the GCF number.
So the greatest common factor 6738 and 6756 is 6.

Also check out the Least Common Multiple of 6738 and 6756