What is the Greatest Common Factor of 13767 and 13780?

Greatest common factor (GCF) of 13767 and 13780 is 13.

GCF(13767,13780) = 13

We will now calculate the prime factors of 13767 and 13780, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 13767 and 13780.

How to find the GCF of 13767 and 13780?

We will first find the prime factorization of 13767 and 13780. After we will calculate the factors of 13767 and 13780 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 13780

Prime factors of 13780 are 2, 5, 13, 53. Prime factorization of 13780 in exponential form is:

13780 = 2² × 5¹ × 13¹ × 53¹

Step-3: Factors of 13767

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

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

Step-4: Factors of 13780

List of positive integer factors of 13780 that divides 13767 without a remainder.

1, 2, 4, 5, 10, 13, 20, 26, 52, 53, 65, 106, 130, 212, 260, 265, 530, 689, 1060, 1378, 2756, 3445, 6890

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 13767 and 13780. The biggest common factor number is the GCF number.
So the greatest common factor 13767 and 13780 is 13.

Also check out the Least Common Multiple of 13767 and 13780