What is the Greatest Common Factor of 13680 and 13690?

Greatest common factor (GCF) of 13680 and 13690 is 10.

GCF(13680,13690) = 10

We will now calculate the prime factors of 13680 and 13690, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 13680 and 13690.

How to find the GCF of 13680 and 13690?

We will first find the prime factorization of 13680 and 13690. After we will calculate the factors of 13680 and 13690 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 13690

Prime factors of 13690 are 2, 5, 37. Prime factorization of 13690 in exponential form is:

13690 = 2¹ × 5¹ × 37²

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 13690

List of positive integer factors of 13690 that divides 13680 without a remainder.

1, 2, 5, 10, 37, 74, 185, 370, 1369, 2738, 6845

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 13680 and 13690. The biggest common factor number is the GCF number.
So the greatest common factor 13680 and 13690 is 10.

Also check out the Least Common Multiple of 13680 and 13690