What is the Greatest Common Factor of 11189 and 11200?

Greatest common factor (GCF) of 11189 and 11200 is 1.

GCF(11189,11200) = 1

We will now calculate the prime factors of 11189 and 11200, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 11189 and 11200.

How to find the GCF of 11189 and 11200?

We will first find the prime factorization of 11189 and 11200. After we will calculate the factors of 11189 and 11200 and find the biggest common factor number .

Step-1: Prime Factorization of 11189

Prime factors of 11189 are 67, 167. Prime factorization of 11189 in exponential form is:

11189 = 67¹ × 167¹

Step-2: Prime Factorization of 11200

Prime factors of 11200 are 2, 5, 7. Prime factorization of 11200 in exponential form is:

11200 = 2⁶ × 5² × 7¹

Step-3: Factors of 11189

List of positive integer factors of 11189 that divides 11189 without a remainder.

1, 67, 167

Step-4: Factors of 11200

List of positive integer factors of 11200 that divides 11189 without a remainder.

1, 2, 4, 5, 7, 8, 10, 14, 16, 20, 25, 28, 32, 35, 40, 50, 56, 64, 70, 80, 100, 112, 140, 160, 175, 200, 224, 280, 320, 350, 400, 448, 560, 700, 800, 1120, 1400, 1600, 2240, 2800, 5600

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 11189 and 11200. The biggest common factor number is the GCF number.
So the greatest common factor 11189 and 11200 is 1.

Also check out the Least Common Multiple of 11189 and 11200