What is the Greatest Common Factor of 13800 and 13812?

Greatest common factor (GCF) of 13800 and 13812 is 12.

GCF(13800,13812) = 12

We will now calculate the prime factors of 13800 and 13812, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 13800 and 13812.

How to find the GCF of 13800 and 13812?

We will first find the prime factorization of 13800 and 13812. After we will calculate the factors of 13800 and 13812 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 13812

Prime factors of 13812 are 2, 3, 1151. Prime factorization of 13812 in exponential form is:

13812 = 2² × 3¹ × 1151¹

Step-3: Factors of 13800

List of positive integer factors of 13800 that divides 13800 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

Step-4: Factors of 13812

List of positive integer factors of 13812 that divides 13800 without a remainder.

1, 2, 3, 4, 6, 12, 1151, 2302, 3453, 4604, 6906

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 13800 and 13812. The biggest common factor number is the GCF number.
So the greatest common factor 13800 and 13812 is 12.

Also check out the Least Common Multiple of 13800 and 13812