What is the Greatest Common Factor of 67584 and 67590?

Greatest common factor (GCF) of 67584 and 67590 is 6.

GCF(67584,67590) = 6

We will now calculate the prime factors of 67584 and 67590, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 67584 and 67590.

How to find the GCF of 67584 and 67590?

We will first find the prime factorization of 67584 and 67590. After we will calculate the factors of 67584 and 67590 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 67590

Prime factors of 67590 are 2, 3, 5, 751. Prime factorization of 67590 in exponential form is:

67590 = 2¹ × 3² × 5¹ × 751¹

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 67590

List of positive integer factors of 67590 that divides 67584 without a remainder.

1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90, 751, 1502, 2253, 3755, 4506, 6759, 7510, 11265, 13518, 22530, 33795

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 67584 and 67590. The biggest common factor number is the GCF number.
So the greatest common factor 67584 and 67590 is 6.

Also check out the Least Common Multiple of 67584 and 67590