What is the Greatest Common Factor of 67300 and 67314?

Greatest common factor (GCF) of 67300 and 67314 is 2.

GCF(67300,67314) = 2

We will now calculate the prime factors of 67300 and 67314, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 67300 and 67314.

How to find the GCF of 67300 and 67314?

We will first find the prime factorization of 67300 and 67314. After we will calculate the factors of 67300 and 67314 and find the biggest common factor number .

Step-1: Prime Factorization of 67300

Prime factors of 67300 are 2, 5, 673. Prime factorization of 67300 in exponential form is:

67300 = 2² × 5² × 673¹

Step-2: Prime Factorization of 67314

Prime factors of 67314 are 2, 3, 13, 863. Prime factorization of 67314 in exponential form is:

67314 = 2¹ × 3¹ × 13¹ × 863¹

Step-3: Factors of 67300

List of positive integer factors of 67300 that divides 67300 without a remainder.

1, 2, 4, 5, 10, 20, 25, 50, 100, 673, 1346, 2692, 3365, 6730, 13460, 16825, 33650

Step-4: Factors of 67314

List of positive integer factors of 67314 that divides 67300 without a remainder.

1, 2, 3, 6, 13, 26, 39, 78, 863, 1726, 2589, 5178, 11219, 22438, 33657

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 67300 and 67314. The biggest common factor number is the GCF number.
So the greatest common factor 67300 and 67314 is 2.

Also check out the Least Common Multiple of 67300 and 67314