What is the Greatest Common Factor of 67584 and 67600?

Greatest common factor (GCF) of 67584 and 67600 is 16.

GCF(67584,67600) = 16

We will now calculate the prime factors of 67584 and 67600, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 67584 and 67600.

How to find the GCF of 67584 and 67600?

We will first find the prime factorization of 67584 and 67600. After we will calculate the factors of 67584 and 67600 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 67600

Prime factors of 67600 are 2, 5, 13. Prime factorization of 67600 in exponential form is:

67600 = 2⁴ × 5² × 13²

Step-3: Factors of 67584

List of positive integer factors of 67584 that divides 67584 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

Step-4: Factors of 67600

List of positive integer factors of 67600 that divides 67584 without a remainder.

1, 2, 4, 5, 8, 10, 13, 16, 20, 25, 26, 40, 50, 52, 65, 80, 100, 104, 130, 169, 200, 208, 260, 325, 338, 400, 520, 650, 676, 845, 1040, 1300, 1352, 1690, 2600, 2704, 3380, 4225, 5200, 6760, 8450, 13520, 16900, 33800

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 67584 and 67600. The biggest common factor number is the GCF number.
So the greatest common factor 67584 and 67600 is 16.

Also check out the Least Common Multiple of 67584 and 67600