What is the Greatest Common Factor of 67200 and 67218?

Greatest common factor (GCF) of 67200 and 67218 is 6.

GCF(67200,67218) = 6

We will now calculate the prime factors of 67200 and 67218, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 67200 and 67218.

How to find the GCF of 67200 and 67218?

We will first find the prime factorization of 67200 and 67218. After we will calculate the factors of 67200 and 67218 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 67218

Prime factors of 67218 are 2, 3, 17, 659. Prime factorization of 67218 in exponential form is:

67218 = 2¹ × 3¹ × 17¹ × 659¹

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 67218

List of positive integer factors of 67218 that divides 67200 without a remainder.

1, 2, 3, 6, 17, 34, 51, 102, 659, 1318, 1977, 3954, 11203, 22406, 33609

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 67200 and 67218. The biggest common factor number is the GCF number.
So the greatest common factor 67200 and 67218 is 6.

Also check out the Least Common Multiple of 67200 and 67218