What is the Greatest Common Factor of 13788 and 13800?

Greatest common factor (GCF) of 13788 and 13800 is 12.

GCF(13788,13800) = 12

We will now calculate the prime factors of 13788 and 13800, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 13788 and 13800.

How to find the GCF of 13788 and 13800?

We will first find the prime factorization of 13788 and 13800. After we will calculate the factors of 13788 and 13800 and find the biggest common factor number .

Step-1: Prime Factorization of 13788

Prime factors of 13788 are 2, 3, 383. Prime factorization of 13788 in exponential form is:

13788 = 2² × 3² × 383¹

Step-2: Prime Factorization of 13800

Prime factors of 13800 are 2, 3, 5, 23. Prime factorization of 13800 in exponential form is:

13800 = 2³ × 3¹ × 5² × 23¹

Step-3: Factors of 13788

List of positive integer factors of 13788 that divides 13788 without a remainder.

1, 2, 3, 4, 6, 9, 12, 18, 36, 383, 766, 1149, 1532, 2298, 3447, 4596, 6894

Step-4: Factors of 13800

List of positive integer factors of 13800 that divides 13788 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 23, 24, 25, 30, 40, 46, 50, 60, 69, 75, 92, 100, 115, 120, 138, 150, 184, 200, 230, 276, 300, 345, 460, 552, 575, 600, 690, 920, 1150, 1380, 1725, 2300, 2760, 3450, 4600, 6900

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 13788 and 13800. The biggest common factor number is the GCF number.
So the greatest common factor 13788 and 13800 is 12.

Also check out the Least Common Multiple of 13788 and 13800