What is the Greatest Common Factor of 600 and 615?

Greatest common factor (GCF) of 600 and 615 is 15.

GCF(600,615) = 15

We will now calculate the prime factors of 600 and 615, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 600 and 615.

How to find the GCF of 600 and 615?

We will first find the prime factorization of 600 and 615. After we will calculate the factors of 600 and 615 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 615

Prime factors of 615 are 3, 5, 41. Prime factorization of 615 in exponential form is:

615 = 3¹ × 5¹ × 41¹

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 615

List of positive integer factors of 615 that divides 600 without a remainder.

1, 3, 5, 15, 41, 123, 205

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 600 and 615. The biggest common factor number is the GCF number.
So the greatest common factor 600 and 615 is 15.

Also check out the Least Common Multiple of 600 and 615