What is the Greatest Common Factor of 13680 and 13698?

Greatest common factor (GCF) of 13680 and 13698 is 18.

GCF(13680,13698) = 18

We will now calculate the prime factors of 13680 and 13698, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 13680 and 13698.

How to find the GCF of 13680 and 13698?

We will first find the prime factorization of 13680 and 13698. After we will calculate the factors of 13680 and 13698 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 13698

Prime factors of 13698 are 2, 3, 761. Prime factorization of 13698 in exponential form is:

13698 = 2¹ × 3² × 761¹

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 13698

List of positive integer factors of 13698 that divides 13680 without a remainder.

1, 2, 3, 6, 9, 18, 761, 1522, 2283, 4566, 6849

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 13680 and 13698. The biggest common factor number is the GCF number.
So the greatest common factor 13680 and 13698 is 18.

Also check out the Least Common Multiple of 13680 and 13698