What is the Greatest Common Factor of 13674 and 13680?

Greatest common factor (GCF) of 13674 and 13680 is 6.

GCF(13674,13680) = 6

We will now calculate the prime factors of 13674 and 13680, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 13674 and 13680.

How to find the GCF of 13674 and 13680?

We will first find the prime factorization of 13674 and 13680. After we will calculate the factors of 13674 and 13680 and find the biggest common factor number .

Step-1: Prime Factorization of 13674

Prime factors of 13674 are 2, 3, 43, 53. Prime factorization of 13674 in exponential form is:

13674 = 2¹ × 3¹ × 43¹ × 53¹

Step-2: 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-3: Factors of 13674

List of positive integer factors of 13674 that divides 13674 without a remainder.

1, 2, 3, 6, 43, 53, 86, 106, 129, 159, 258, 318, 2279, 4558, 6837

Step-4: Factors of 13680

List of positive integer factors of 13680 that divides 13674 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 13674 and 13680. The biggest common factor number is the GCF number.
So the greatest common factor 13674 and 13680 is 6.

Also check out the Least Common Multiple of 13674 and 13680