What is the Greatest Common Factor of 13680 and 13689?

Greatest common factor (GCF) of 13680 and 13689 is 9.

GCF(13680,13689) = 9

We will now calculate the prime factors of 13680 and 13689, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 13680 and 13689.

How to find the GCF of 13680 and 13689?

We will first find the prime factorization of 13680 and 13689. After we will calculate the factors of 13680 and 13689 and find the biggest common factor number .

Step-1: Prime Factorization of 13680

Prime factors of 13680 are 2, 3, 5, 19. Prime factorization of 13680 in exponential form is:

13680 = 2⁴ × 3² × 5¹ × 19¹

Step-2: Prime Factorization of 13689

Prime factors of 13689 are 3, 13. Prime factorization of 13689 in exponential form is:

13689 = 3⁴ × 13²

Step-3: Factors of 13680

List of positive integer factors of 13680 that divides 13680 without a remainder.

1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 19, 20, 24, 30, 36, 38, 40, 45, 48, 57, 60, 72, 76, 80, 90, 95, 114, 120, 144, 152, 171, 180, 190, 228, 240, 285, 304, 342, 360, 380, 456, 570, 684, 720, 760, 855, 912, 1140, 1368, 1520, 1710, 2280, 2736, 3420, 4560, 6840

Step-4: Factors of 13689

List of positive integer factors of 13689 that divides 13680 without a remainder.

1, 3, 9, 13, 27, 39, 81, 117, 169, 351, 507, 1053, 1521, 4563

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 13680 and 13689. The biggest common factor number is the GCF number.
So the greatest common factor 13680 and 13689 is 9.

Also check out the Least Common Multiple of 13680 and 13689