What is the Greatest Common Factor of 564 and 576?

Greatest common factor (GCF) of 564 and 576 is 12.

GCF(564,576) = 12

We will now calculate the prime factors of 564 and 576, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 564 and 576.

How to find the GCF of 564 and 576?

We will first find the prime factorization of 564 and 576. After we will calculate the factors of 564 and 576 and find the biggest common factor number .

Step-1: Prime Factorization of 564

Prime factors of 564 are 2, 3, 47. Prime factorization of 564 in exponential form is:

564 = 2² × 3¹ × 47¹

Step-2: Prime Factorization of 576

Prime factors of 576 are 2, 3. Prime factorization of 576 in exponential form is:

576 = 2⁶ × 3²

Step-3: Factors of 564

List of positive integer factors of 564 that divides 564 without a remainder.

1, 2, 3, 4, 6, 12, 47, 94, 141, 188, 282

Step-4: Factors of 576

List of positive integer factors of 576 that divides 564 without a remainder.

1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 64, 72, 96, 144, 192, 288

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 564 and 576. The biggest common factor number is the GCF number.
So the greatest common factor 564 and 576 is 12.

Also check out the Least Common Multiple of 564 and 576