What is the Greatest Common Factor of 67200 and 67208?

Greatest common factor (GCF) of 67200 and 67208 is 8.

GCF(67200,67208) = 8

We will now calculate the prime factors of 67200 and 67208, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 67200 and 67208.

How to find the GCF of 67200 and 67208?

We will first find the prime factorization of 67200 and 67208. After we will calculate the factors of 67200 and 67208 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 67208

Prime factors of 67208 are 2, 31, 271. Prime factorization of 67208 in exponential form is:

67208 = 2³ × 31¹ × 271¹

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 67208

List of positive integer factors of 67208 that divides 67200 without a remainder.

1, 2, 4, 8, 31, 62, 124, 248, 271, 542, 1084, 2168, 8401, 16802, 33604

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 67200 and 67208. The biggest common factor number is the GCF number.
So the greatest common factor 67200 and 67208 is 8.

Also check out the Least Common Multiple of 67200 and 67208