What is the Greatest Common Factor of 13842 and 13860?

Greatest common factor (GCF) of 13842 and 13860 is 18.

GCF(13842,13860) = 18

We will now calculate the prime factors of 13842 and 13860, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 13842 and 13860.

How to find the GCF of 13842 and 13860?

We will first find the prime factorization of 13842 and 13860. After we will calculate the factors of 13842 and 13860 and find the biggest common factor number .

Step-1: Prime Factorization of 13842

Prime factors of 13842 are 2, 3, 769. Prime factorization of 13842 in exponential form is:

13842 = 2¹ × 3² × 769¹

Step-2: 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-3: Factors of 13842

List of positive integer factors of 13842 that divides 13842 without a remainder.

1, 2, 3, 6, 9, 18, 769, 1538, 2307, 4614, 6921

Step-4: Factors of 13860

List of positive integer factors of 13860 that divides 13842 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 13842 and 13860. The biggest common factor number is the GCF number.
So the greatest common factor 13842 and 13860 is 18.

Also check out the Least Common Multiple of 13842 and 13860