What is the Greatest Common Factor of 82314 and 82334?

Greatest common factor (GCF) of 82314 and 82334 is 2.

GCF(82314,82334) = 2

We will now calculate the prime factors of 82314 and 82334, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 82314 and 82334.

How to find the GCF of 82314 and 82334?

We will first find the prime factorization of 82314 and 82334. After we will calculate the factors of 82314 and 82334 and find the biggest common factor number .

Step-1: Prime Factorization of 82314

Prime factors of 82314 are 2, 3, 17, 269. Prime factorization of 82314 in exponential form is:

82314 = 2¹ × 3² × 17¹ × 269¹

Step-2: Prime Factorization of 82334

Prime factors of 82334 are 2, 7, 5881. Prime factorization of 82334 in exponential form is:

82334 = 2¹ × 7¹ × 5881¹

Step-3: Factors of 82314

List of positive integer factors of 82314 that divides 82314 without a remainder.

1, 2, 3, 6, 9, 17, 18, 34, 51, 102, 153, 269, 306, 538, 807, 1614, 2421, 4573, 4842, 9146, 13719, 27438, 41157

Step-4: Factors of 82334

List of positive integer factors of 82334 that divides 82314 without a remainder.

1, 2, 7, 14, 5881, 11762, 41167

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 82314 and 82334. The biggest common factor number is the GCF number.
So the greatest common factor 82314 and 82334 is 2.

Also check out the Least Common Multiple of 82314 and 82334