What is the Greatest Common Factor of 67200 and 67206?

Greatest common factor (GCF) of 67200 and 67206 is 6.

GCF(67200,67206) = 6

We will now calculate the prime factors of 67200 and 67206, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 67200 and 67206.

How to find the GCF of 67200 and 67206?

We will first find the prime factorization of 67200 and 67206. After we will calculate the factors of 67200 and 67206 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 67206

Prime factors of 67206 are 2, 3, 23, 487. Prime factorization of 67206 in exponential form is:

67206 = 2¹ × 3¹ × 23¹ × 487¹

Step-3: Factors of 67200

List of positive integer factors of 67200 that divides 67200 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

Step-4: Factors of 67206

List of positive integer factors of 67206 that divides 67200 without a remainder.

1, 2, 3, 6, 23, 46, 69, 138, 487, 974, 1461, 2922, 11201, 22402, 33603

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 67200 and 67206. The biggest common factor number is the GCF number.
So the greatest common factor 67200 and 67206 is 6.

Also check out the Least Common Multiple of 67200 and 67206