What is the Greatest Common Factor of 600 and 614?

Greatest common factor (GCF) of 600 and 614 is 2.

GCF(600,614) = 2

We will now calculate the prime factors of 600 and 614, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 600 and 614.

How to find the GCF of 600 and 614?

We will first find the prime factorization of 600 and 614. After we will calculate the factors of 600 and 614 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 614

Prime factors of 614 are 2, 307. Prime factorization of 614 in exponential form is:

614 = 2¹ × 307¹

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 614

List of positive integer factors of 614 that divides 600 without a remainder.

1, 2, 307

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 600 and 614. The biggest common factor number is the GCF number.
So the greatest common factor 600 and 614 is 2.

Also check out the Least Common Multiple of 600 and 614