What is the Greatest Common Factor of 1565 and 1584?

Greatest common factor (GCF) of 1565 and 1584 is 1.

GCF(1565,1584) = 1

We will now calculate the prime factors of 1565 and 1584, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1565 and 1584.

How to find the GCF of 1565 and 1584?

We will first find the prime factorization of 1565 and 1584. After we will calculate the factors of 1565 and 1584 and find the biggest common factor number .

Step-1: Prime Factorization of 1565

Prime factors of 1565 are 5, 313. Prime factorization of 1565 in exponential form is:

1565 = 5¹ × 313¹

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 1565

List of positive integer factors of 1565 that divides 1565 without a remainder.

1, 5, 313

Step-4: Factors of 1584

List of positive integer factors of 1584 that divides 1565 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 1565 and 1584. The biggest common factor number is the GCF number.
So the greatest common factor 1565 and 1584 is 1.

Also check out the Least Common Multiple of 1565 and 1584