What is the Greatest Common Factor of 1569 and 1584?

Greatest common factor (GCF) of 1569 and 1584 is 3.

GCF(1569,1584) = 3

We will now calculate the prime factors of 1569 and 1584, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1569 and 1584.

How to find the GCF of 1569 and 1584?

We will first find the prime factorization of 1569 and 1584. After we will calculate the factors of 1569 and 1584 and find the biggest common factor number .

Step-1: Prime Factorization of 1569

Prime factors of 1569 are 3, 523. Prime factorization of 1569 in exponential form is:

1569 = 3¹ × 523¹

Step-2: Prime Factorization of 1584

Prime factors of 1584 are 2, 3, 11. Prime factorization of 1584 in exponential form is:

1584 = 2⁴ × 3² × 11¹

Step-3: Factors of 1569

List of positive integer factors of 1569 that divides 1569 without a remainder.

1, 3, 523

Step-4: Factors of 1584

List of positive integer factors of 1584 that divides 1569 without a remainder.

1, 2, 3, 4, 6, 8, 9, 11, 12, 16, 18, 22, 24, 33, 36, 44, 48, 66, 72, 88, 99, 132, 144, 176, 198, 264, 396, 528, 792

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1569 and 1584. The biggest common factor number is the GCF number.
So the greatest common factor 1569 and 1584 is 3.

Also check out the Least Common Multiple of 1569 and 1584