What is the Greatest Common Factor of 67575 and 67584?

Greatest common factor (GCF) of 67575 and 67584 is 3.

GCF(67575,67584) = 3

We will now calculate the prime factors of 67575 and 67584, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 67575 and 67584.

How to find the GCF of 67575 and 67584?

We will first find the prime factorization of 67575 and 67584. After we will calculate the factors of 67575 and 67584 and find the biggest common factor number .

Step-1: Prime Factorization of 67575

Prime factors of 67575 are 3, 5, 17, 53. Prime factorization of 67575 in exponential form is:

67575 = 3¹ × 5² × 17¹ × 53¹

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 67575

List of positive integer factors of 67575 that divides 67575 without a remainder.

1, 3, 5, 15, 17, 25, 51, 53, 75, 85, 159, 255, 265, 425, 795, 901, 1275, 1325, 2703, 3975, 4505, 13515, 22525

Step-4: Factors of 67584

List of positive integer factors of 67584 that divides 67575 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 67575 and 67584. The biggest common factor number is the GCF number.
So the greatest common factor 67575 and 67584 is 3.

Also check out the Least Common Multiple of 67575 and 67584