What is the Greatest Common Factor of 67200 and 67219?

Greatest common factor (GCF) of 67200 and 67219 is 1.

GCF(67200,67219) = 1

We will now calculate the prime factors of 67200 and 67219, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 67200 and 67219.

How to find the GCF of 67200 and 67219?

We will first find the prime factorization of 67200 and 67219. After we will calculate the factors of 67200 and 67219 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 67219

Prime factors of 67219 are 67219. Prime factorization of 67219 in exponential form is:

67219 = 67219¹

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 67219

List of positive integer factors of 67219 that divides 67200 without a remainder.

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 67200 and 67219. The biggest common factor number is the GCF number.
So the greatest common factor 67200 and 67219 is 1.

Also check out the Least Common Multiple of 67200 and 67219