What is the Greatest Common Factor of 586 and 590?

Greatest common factor (GCF) of 586 and 590 is 2.

GCF(586,590) = 2

We will now calculate the prime factors of 586 and 590, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 586 and 590.

How to find the GCF of 586 and 590?

We will first find the prime factorization of 586 and 590. After we will calculate the factors of 586 and 590 and find the biggest common factor number .

Step-1: Prime Factorization of 586

Prime factors of 586 are 2, 293. Prime factorization of 586 in exponential form is:

586 = 2¹ × 293¹

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 586

List of positive integer factors of 586 that divides 586 without a remainder.

1, 2, 293

Step-4: Factors of 590

List of positive integer factors of 590 that divides 586 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 586 and 590. The biggest common factor number is the GCF number.
So the greatest common factor 586 and 590 is 2.

Also check out the Least Common Multiple of 586 and 590