What is the Greatest Common Factor of 585 and 590?

Greatest common factor (GCF) of 585 and 590 is 5.

GCF(585,590) = 5

We will now calculate the prime factors of 585 and 590, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 585 and 590.

How to find the GCF of 585 and 590?

We will first find the prime factorization of 585 and 590. After we will calculate the factors of 585 and 590 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 590

Prime factors of 590 are 2, 5, 59. Prime factorization of 590 in exponential form is:

590 = 2¹ × 5¹ × 59¹

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 590

List of positive integer factors of 590 that divides 585 without a remainder.

1, 2, 5, 10, 59, 118, 295

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 585 and 590. The biggest common factor number is the GCF number.
So the greatest common factor 585 and 590 is 5.

Also check out the Least Common Multiple of 585 and 590