What is the Greatest Common Factor of 13749 and 13767?

Greatest common factor (GCF) of 13749 and 13767 is 3.

GCF(13749,13767) = 3

We will now calculate the prime factors of 13749 and 13767, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 13749 and 13767.

How to find the GCF of 13749 and 13767?

We will first find the prime factorization of 13749 and 13767. After we will calculate the factors of 13749 and 13767 and find the biggest common factor number .

Step-1: Prime Factorization of 13749

Prime factors of 13749 are 3, 4583. Prime factorization of 13749 in exponential form is:

13749 = 3¹ × 4583¹

Step-2: Prime Factorization of 13767

Prime factors of 13767 are 3, 13, 353. Prime factorization of 13767 in exponential form is:

13767 = 3¹ × 13¹ × 353¹

Step-3: Factors of 13749

List of positive integer factors of 13749 that divides 13749 without a remainder.

1, 3, 4583

Step-4: Factors of 13767

List of positive integer factors of 13767 that divides 13749 without a remainder.

1, 3, 13, 39, 353, 1059, 4589

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 13749 and 13767. The biggest common factor number is the GCF number.
So the greatest common factor 13749 and 13767 is 3.

Also check out the Least Common Multiple of 13749 and 13767