What is the Greatest Common Factor of 1188 and 1200?

Greatest common factor (GCF) of 1188 and 1200 is 12.

GCF(1188,1200) = 12

We will now calculate the prime factors of 1188 and 1200, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1188 and 1200.

How to find the GCF of 1188 and 1200?

We will first find the prime factorization of 1188 and 1200. After we will calculate the factors of 1188 and 1200 and find the biggest common factor number .

Step-1: Prime Factorization of 1188

Prime factors of 1188 are 2, 3, 11. Prime factorization of 1188 in exponential form is:

1188 = 2² × 3³ × 11¹

Step-2: Prime Factorization of 1200

Prime factors of 1200 are 2, 3, 5. Prime factorization of 1200 in exponential form is:

1200 = 2⁴ × 3¹ × 5²

Step-3: Factors of 1188

List of positive integer factors of 1188 that divides 1188 without a remainder.

1, 2, 3, 4, 6, 9, 11, 12, 18, 22, 27, 33, 36, 44, 54, 66, 99, 108, 132, 198, 297, 396, 594

Step-4: Factors of 1200

List of positive integer factors of 1200 that divides 1188 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 25, 30, 40, 48, 50, 60, 75, 80, 100, 120, 150, 200, 240, 300, 400, 600

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1188 and 1200. The biggest common factor number is the GCF number.
So the greatest common factor 1188 and 1200 is 12.

Also check out the Least Common Multiple of 1188 and 1200