What is the Greatest Common Factor of 67569 and 67584?

Greatest common factor (GCF) of 67569 and 67584 is 3.

GCF(67569,67584) = 3

We will now calculate the prime factors of 67569 and 67584, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 67569 and 67584.

How to find the GCF of 67569 and 67584?

We will first find the prime factorization of 67569 and 67584. After we will calculate the factors of 67569 and 67584 and find the biggest common factor number .

Step-1: Prime Factorization of 67569

Prime factors of 67569 are 3, 101, 223. Prime factorization of 67569 in exponential form is:

67569 = 3¹ × 101¹ × 223¹

Step-2: Prime Factorization of 67584

Prime factors of 67584 are 2, 3, 11. Prime factorization of 67584 in exponential form is:

67584 = 2¹¹ × 3¹ × 11¹

Step-3: Factors of 67569

List of positive integer factors of 67569 that divides 67569 without a remainder.

1, 3, 101, 223, 303, 669, 22523

Step-4: Factors of 67584

List of positive integer factors of 67584 that divides 67569 without a remainder.

1, 2, 3, 4, 6, 8, 11, 12, 16, 22, 24, 32, 33, 44, 48, 64, 66, 88, 96, 128, 132, 176, 192, 256, 264, 352, 384, 512, 528, 704, 768, 1024, 1056, 1408, 1536, 2048, 2112, 2816, 3072, 4224, 5632, 6144, 8448, 11264, 16896, 22528, 33792

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 67569 and 67584. The biggest common factor number is the GCF number.
So the greatest common factor 67569 and 67584 is 3.

Also check out the Least Common Multiple of 67569 and 67584