What is the Greatest Common Factor of 586 and 600?

Greatest common factor (GCF) of 586 and 600 is 2.

GCF(586,600) = 2

We will now calculate the prime factors of 586 and 600, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 586 and 600.

How to find the GCF of 586 and 600?

We will first find the prime factorization of 586 and 600. After we will calculate the factors of 586 and 600 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 600

Prime factors of 600 are 2, 3, 5. Prime factorization of 600 in exponential form is:

600 = 2³ × 3¹ × 5²

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 600

List of positive integer factors of 600 that divides 586 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 25, 30, 40, 50, 60, 75, 100, 120, 150, 200, 300

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 586 and 600. The biggest common factor number is the GCF number.
So the greatest common factor 586 and 600 is 2.

Also check out the Least Common Multiple of 586 and 600