What is the Greatest Common Factor of 585 and 595?

Greatest common factor (GCF) of 585 and 595 is 5.

GCF(585,595) = 5

We will now calculate the prime factors of 585 and 595, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 585 and 595.

How to find the GCF of 585 and 595?

We will first find the prime factorization of 585 and 595. After we will calculate the factors of 585 and 595 and find the biggest common factor number .

Step-1: Prime Factorization of 585

Prime factors of 585 are 3, 5, 13. Prime factorization of 585 in exponential form is:

585 = 3² × 5¹ × 13¹

Step-2: Prime Factorization of 595

Prime factors of 595 are 5, 7, 17. Prime factorization of 595 in exponential form is:

595 = 5¹ × 7¹ × 17¹

Step-3: Factors of 585

List of positive integer factors of 585 that divides 585 without a remainder.

1, 3, 5, 9, 13, 15, 39, 45, 65, 117, 195

Step-4: Factors of 595

List of positive integer factors of 595 that divides 585 without a remainder.

1, 5, 7, 17, 35, 85, 119

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 585 and 595. The biggest common factor number is the GCF number.
So the greatest common factor 585 and 595 is 5.

Also check out the Least Common Multiple of 585 and 595