What is the Greatest Common Factor of 13860 and 13874?

Greatest common factor (GCF) of 13860 and 13874 is 14.

GCF(13860,13874) = 14

We will now calculate the prime factors of 13860 and 13874, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 13860 and 13874.

How to find the GCF of 13860 and 13874?

We will first find the prime factorization of 13860 and 13874. After we will calculate the factors of 13860 and 13874 and find the biggest common factor number .

Step-1: Prime Factorization of 13860

Prime factors of 13860 are 2, 3, 5, 7, 11. Prime factorization of 13860 in exponential form is:

13860 = 2² × 3² × 5¹ × 7¹ × 11¹

Step-2: Prime Factorization of 13874

Prime factors of 13874 are 2, 7, 991. Prime factorization of 13874 in exponential form is:

13874 = 2¹ × 7¹ × 991¹

Step-3: Factors of 13860

List of positive integer factors of 13860 that divides 13860 without a remainder.

1, 2, 3, 4, 5, 6, 7, 9, 10, 11, 12, 14, 15, 18, 20, 21, 22, 28, 30, 33, 35, 36, 42, 44, 45, 55, 60, 63, 66, 70, 77, 84, 90, 99, 105, 110, 126, 132, 140, 154, 165, 180, 198, 210, 220, 231, 252, 308, 315, 330, 385, 396, 420, 462, 495, 630, 660, 693, 770, 924, 990, 1155, 1260, 1386, 1540, 1980, 2310, 2772, 3465, 4620, 6930

Step-4: Factors of 13874

List of positive integer factors of 13874 that divides 13860 without a remainder.

1, 2, 7, 14, 991, 1982, 6937

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 13860 and 13874. The biggest common factor number is the GCF number.
So the greatest common factor 13860 and 13874 is 14.

Also check out the Least Common Multiple of 13860 and 13874