What is the Greatest Common Factor of 11186 and 11200?

Greatest common factor (GCF) of 11186 and 11200 is 14.

GCF(11186,11200) = 14

We will now calculate the prime factors of 11186 and 11200, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 11186 and 11200.

How to find the GCF of 11186 and 11200?

We will first find the prime factorization of 11186 and 11200. After we will calculate the factors of 11186 and 11200 and find the biggest common factor number .

Step-1: Prime Factorization of 11186

Prime factors of 11186 are 2, 7, 17, 47. Prime factorization of 11186 in exponential form is:

11186 = 2¹ × 7¹ × 17¹ × 47¹

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 11186

List of positive integer factors of 11186 that divides 11186 without a remainder.

1, 2, 7, 14, 17, 34, 47, 94, 119, 238, 329, 658, 799, 1598, 5593

Step-4: Factors of 11200

List of positive integer factors of 11200 that divides 11186 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 11186 and 11200. The biggest common factor number is the GCF number.
So the greatest common factor 11186 and 11200 is 14.

Also check out the Least Common Multiple of 11186 and 11200