What is the Greatest Common Factor of 67186 and 67200?

Greatest common factor (GCF) of 67186 and 67200 is 14.

GCF(67186,67200) = 14

We will now calculate the prime factors of 67186 and 67200, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 67186 and 67200.

How to find the GCF of 67186 and 67200?

We will first find the prime factorization of 67186 and 67200. After we will calculate the factors of 67186 and 67200 and find the biggest common factor number .

Step-1: Prime Factorization of 67186

Prime factors of 67186 are 2, 7, 4799. Prime factorization of 67186 in exponential form is:

67186 = 2¹ × 7¹ × 4799¹

Step-2: Prime Factorization of 67200

Prime factors of 67200 are 2, 3, 5, 7. Prime factorization of 67200 in exponential form is:

67200 = 2⁷ × 3¹ × 5² × 7¹

Step-3: Factors of 67186

List of positive integer factors of 67186 that divides 67186 without a remainder.

1, 2, 7, 14, 4799, 9598, 33593

Step-4: Factors of 67200

List of positive integer factors of 67200 that divides 67186 without a remainder.

1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 16, 20, 21, 24, 25, 28, 30, 32, 35, 40, 42, 48, 50, 56, 60, 64, 70, 75, 80, 84, 96, 100, 105, 112, 120, 128, 140, 150, 160, 168, 175, 192, 200, 210, 224, 240, 280, 300, 320, 336, 350, 384, 400, 420, 448, 480, 525, 560, 600, 640, 672, 700, 800, 840, 896, 960, 1050, 1120, 1200, 1344, 1400, 1600, 1680, 1920, 2100, 2240, 2400, 2688, 2800, 3200, 3360, 4200, 4480, 4800, 5600, 6720, 8400, 9600, 11200, 13440, 16800, 22400, 33600

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 67186 and 67200. The biggest common factor number is the GCF number.
So the greatest common factor 67186 and 67200 is 14.

Also check out the Least Common Multiple of 67186 and 67200