What is the Greatest Common Factor of 6294 and 6300?

Greatest common factor (GCF) of 6294 and 6300 is 6.

GCF(6294,6300) = 6

We will now calculate the prime factors of 6294 and 6300, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 6294 and 6300.

How to find the GCF of 6294 and 6300?

We will first find the prime factorization of 6294 and 6300. After we will calculate the factors of 6294 and 6300 and find the biggest common factor number .

Step-1: Prime Factorization of 6294

Prime factors of 6294 are 2, 3, 1049. Prime factorization of 6294 in exponential form is:

6294 = 2¹ × 3¹ × 1049¹

Step-2: Prime Factorization of 6300

Prime factors of 6300 are 2, 3, 5, 7. Prime factorization of 6300 in exponential form is:

6300 = 2² × 3² × 5² × 7¹

Step-3: Factors of 6294

List of positive integer factors of 6294 that divides 6294 without a remainder.

1, 2, 3, 6, 1049, 2098, 3147

Step-4: Factors of 6300

List of positive integer factors of 6300 that divides 6294 without a remainder.

1, 2, 3, 4, 5, 6, 7, 9, 10, 12, 14, 15, 18, 20, 21, 25, 28, 30, 35, 36, 42, 45, 50, 60, 63, 70, 75, 84, 90, 100, 105, 126, 140, 150, 175, 180, 210, 225, 252, 300, 315, 350, 420, 450, 525, 630, 700, 900, 1050, 1260, 1575, 2100, 3150

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 6294 and 6300. The biggest common factor number is the GCF number.
So the greatest common factor 6294 and 6300 is 6.

Also check out the Least Common Multiple of 6294 and 6300