What is the Greatest Common Factor of 6723 and 6729?

Greatest common factor (GCF) of 6723 and 6729 is 3.

GCF(6723,6729) = 3

We will now calculate the prime factors of 6723 and 6729, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 6723 and 6729.

How to find the GCF of 6723 and 6729?

We will first find the prime factorization of 6723 and 6729. After we will calculate the factors of 6723 and 6729 and find the biggest common factor number .

Step-1: Prime Factorization of 6723

Prime factors of 6723 are 3, 83. Prime factorization of 6723 in exponential form is:

6723 = 3⁴ × 83¹

Step-2: Prime Factorization of 6729

Prime factors of 6729 are 3, 2243. Prime factorization of 6729 in exponential form is:

6729 = 3¹ × 2243¹

Step-3: Factors of 6723

List of positive integer factors of 6723 that divides 6723 without a remainder.

1, 3, 9, 27, 81, 83, 249, 747, 2241

Step-4: Factors of 6729

List of positive integer factors of 6729 that divides 6723 without a remainder.

1, 3, 2243

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 6723 and 6729. The biggest common factor number is the GCF number.
So the greatest common factor 6723 and 6729 is 3.

Also check out the Least Common Multiple of 6723 and 6729