What is the Greatest Common Factor of 584 and 600?

Greatest common factor (GCF) of 584 and 600 is 8.

GCF(584,600) = 8

We will now calculate the prime factors of 584 and 600, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 584 and 600.

How to find the GCF of 584 and 600?

We will first find the prime factorization of 584 and 600. After we will calculate the factors of 584 and 600 and find the biggest common factor number .

Step-1: Prime Factorization of 584

Prime factors of 584 are 2, 73. Prime factorization of 584 in exponential form is:

584 = 2³ × 73¹

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 584

List of positive integer factors of 584 that divides 584 without a remainder.

1, 2, 4, 8, 73, 146, 292

Step-4: Factors of 600

List of positive integer factors of 600 that divides 584 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 584 and 600. The biggest common factor number is the GCF number.
So the greatest common factor 584 and 600 is 8.

Also check out the Least Common Multiple of 584 and 600