What is the Greatest Common Factor of 564 and 584?

Greatest common factor (GCF) of 564 and 584 is 4.

GCF(564,584) = 4

We will now calculate the prime factors of 564 and 584, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 564 and 584.

How to find the GCF of 564 and 584?

We will first find the prime factorization of 564 and 584. After we will calculate the factors of 564 and 584 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 584

Prime factors of 584 are 2, 73. Prime factorization of 584 in exponential form is:

584 = 2³ × 73¹

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 584

List of positive integer factors of 584 that divides 564 without a remainder.

1, 2, 4, 8, 73, 146, 292

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 564 and 584. The biggest common factor number is the GCF number.
So the greatest common factor 564 and 584 is 4.

Also check out the Least Common Multiple of 564 and 584