What is the Greatest Common Factor of 67301 and 67314?

Greatest common factor (GCF) of 67301 and 67314 is 13.

GCF(67301,67314) = 13

We will now calculate the prime factors of 67301 and 67314, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 67301 and 67314.

How to find the GCF of 67301 and 67314?

We will first find the prime factorization of 67301 and 67314. After we will calculate the factors of 67301 and 67314 and find the biggest common factor number .

Step-1: Prime Factorization of 67301

Prime factors of 67301 are 13, 31, 167. Prime factorization of 67301 in exponential form is:

67301 = 13¹ × 31¹ × 167¹

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 67301

List of positive integer factors of 67301 that divides 67301 without a remainder.

1, 13, 31, 167, 403, 2171, 5177

Step-4: Factors of 67314

List of positive integer factors of 67314 that divides 67301 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 67301 and 67314. The biggest common factor number is the GCF number.
So the greatest common factor 67301 and 67314 is 13.

Also check out the Least Common Multiple of 67301 and 67314