What is the Greatest Common Factor of 565 and 582?

Greatest common factor (GCF) of 565 and 582 is 1.

GCF(565,582) = 1

We will now calculate the prime factors of 565 and 582, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 565 and 582.

How to find the GCF of 565 and 582?

We will first find the prime factorization of 565 and 582. After we will calculate the factors of 565 and 582 and find the biggest common factor number .

Step-1: Prime Factorization of 565

Prime factors of 565 are 5, 113. Prime factorization of 565 in exponential form is:

565 = 5¹ × 113¹

Step-2: Prime Factorization of 582

Prime factors of 582 are 2, 3, 97. Prime factorization of 582 in exponential form is:

582 = 2¹ × 3¹ × 97¹

Step-3: Factors of 565

List of positive integer factors of 565 that divides 565 without a remainder.

1, 5, 113

Step-4: Factors of 582

List of positive integer factors of 582 that divides 565 without a remainder.

1, 2, 3, 6, 97, 194, 291

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 565 and 582. The biggest common factor number is the GCF number.
So the greatest common factor 565 and 582 is 1.

Also check out the Least Common Multiple of 565 and 582