What is the Greatest Common Factor of 600 and 616?

Greatest common factor (GCF) of 600 and 616 is 8.

GCF(600,616) = 8

We will now calculate the prime factors of 600 and 616, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 600 and 616.

How to find the GCF of 600 and 616?

We will first find the prime factorization of 600 and 616. After we will calculate the factors of 600 and 616 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 616

Prime factors of 616 are 2, 7, 11. Prime factorization of 616 in exponential form is:

616 = 2³ × 7¹ × 11¹

Step-3: Factors of 600

List of positive integer factors of 600 that divides 600 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

Step-4: Factors of 616

List of positive integer factors of 616 that divides 600 without a remainder.

1, 2, 4, 7, 8, 11, 14, 22, 28, 44, 56, 77, 88, 154, 308

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 600 and 616. The biggest common factor number is the GCF number.
So the greatest common factor 600 and 616 is 8.

Also check out the Least Common Multiple of 600 and 616