What is the Greatest Common Factor of 595 and 600?

Greatest common factor (GCF) of 595 and 600 is 5.

GCF(595,600) = 5

We will now calculate the prime factors of 595 and 600, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 595 and 600.

How to find the GCF of 595 and 600?

We will first find the prime factorization of 595 and 600. After we will calculate the factors of 595 and 600 and find the biggest common factor number .

Step-1: Prime Factorization of 595

Prime factors of 595 are 5, 7, 17. Prime factorization of 595 in exponential form is:

595 = 5¹ × 7¹ × 17¹

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 595

List of positive integer factors of 595 that divides 595 without a remainder.

1, 5, 7, 17, 35, 85, 119

Step-4: Factors of 600

List of positive integer factors of 600 that divides 595 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 595 and 600. The biggest common factor number is the GCF number.
So the greatest common factor 595 and 600 is 5.

Also check out the Least Common Multiple of 595 and 600