What is the Greatest Common Factor of 565 and 570?

Greatest common factor (GCF) of 565 and 570 is 5.

GCF(565,570) = 5

We will now calculate the prime factors of 565 and 570, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 565 and 570.

How to find the GCF of 565 and 570?

We will first find the prime factorization of 565 and 570. After we will calculate the factors of 565 and 570 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 570

Prime factors of 570 are 2, 3, 5, 19. Prime factorization of 570 in exponential form is:

570 = 2¹ × 3¹ × 5¹ × 19¹

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 570

List of positive integer factors of 570 that divides 565 without a remainder.

1, 2, 3, 5, 6, 10, 15, 19, 30, 38, 57, 95, 114, 190, 285

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 565 and 570. The biggest common factor number is the GCF number.
So the greatest common factor 565 and 570 is 5.

Also check out the Least Common Multiple of 565 and 570