What is the Greatest Common Factor of 1184 and 1200?

Greatest common factor (GCF) of 1184 and 1200 is 16.

GCF(1184,1200) = 16

We will now calculate the prime factors of 1184 and 1200, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1184 and 1200.

How to find the GCF of 1184 and 1200?

We will first find the prime factorization of 1184 and 1200. After we will calculate the factors of 1184 and 1200 and find the biggest common factor number .

Step-1: Prime Factorization of 1184

Prime factors of 1184 are 2, 37. Prime factorization of 1184 in exponential form is:

1184 = 2⁵ × 37¹

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 1184

List of positive integer factors of 1184 that divides 1184 without a remainder.

1, 2, 4, 8, 16, 32, 37, 74, 148, 296, 592

Step-4: Factors of 1200

List of positive integer factors of 1200 that divides 1184 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 1184 and 1200. The biggest common factor number is the GCF number.
So the greatest common factor 1184 and 1200 is 16.

Also check out the Least Common Multiple of 1184 and 1200