What is the Greatest Common Factor of 13860 and 13875?

Greatest common factor (GCF) of 13860 and 13875 is 15.

GCF(13860,13875) = 15

We will now calculate the prime factors of 13860 and 13875, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 13860 and 13875.

How to find the GCF of 13860 and 13875?

We will first find the prime factorization of 13860 and 13875. After we will calculate the factors of 13860 and 13875 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 13875

Prime factors of 13875 are 3, 5, 37. Prime factorization of 13875 in exponential form is:

13875 = 3¹ × 5³ × 37¹

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 13875

List of positive integer factors of 13875 that divides 13860 without a remainder.

1, 3, 5, 15, 25, 37, 75, 111, 125, 185, 375, 555, 925, 2775, 4625

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 13860 and 13875. The biggest common factor number is the GCF number.
So the greatest common factor 13860 and 13875 is 15.

Also check out the Least Common Multiple of 13860 and 13875