What is the Greatest Common Factor of 67184 and 67200?

Greatest common factor (GCF) of 67184 and 67200 is 16.

GCF(67184,67200) = 16

We will now calculate the prime factors of 67184 and 67200, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 67184 and 67200.

How to find the GCF of 67184 and 67200?

We will first find the prime factorization of 67184 and 67200. After we will calculate the factors of 67184 and 67200 and find the biggest common factor number .

Step-1: Prime Factorization of 67184

Prime factors of 67184 are 2, 13, 17, 19. Prime factorization of 67184 in exponential form is:

67184 = 2⁴ × 13¹ × 17¹ × 19¹

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 67184

List of positive integer factors of 67184 that divides 67184 without a remainder.

1, 2, 4, 8, 13, 16, 17, 19, 26, 34, 38, 52, 68, 76, 104, 136, 152, 208, 221, 247, 272, 304, 323, 442, 494, 646, 884, 988, 1292, 1768, 1976, 2584, 3536, 3952, 4199, 5168, 8398, 16796, 33592

Step-4: Factors of 67200

List of positive integer factors of 67200 that divides 67184 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 67184 and 67200. The biggest common factor number is the GCF number.
So the greatest common factor 67184 and 67200 is 16.

Also check out the Least Common Multiple of 67184 and 67200