What is the Greatest Common Factor of 82314 and 82321?

Greatest common factor (GCF) of 82314 and 82321 is 1.

GCF(82314,82321) = 1

We will now calculate the prime factors of 82314 and 82321, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 82314 and 82321.

How to find the GCF of 82314 and 82321?

We will first find the prime factorization of 82314 and 82321. After we will calculate the factors of 82314 and 82321 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 82321

Prime factors of 82321 are 191, 431. Prime factorization of 82321 in exponential form is:

82321 = 191¹ × 431¹

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 82321

List of positive integer factors of 82321 that divides 82314 without a remainder.

1, 191, 431

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 82314 and 82321. The biggest common factor number is the GCF number.
So the greatest common factor 82314 and 82321 is 1.

Also check out the Least Common Multiple of 82314 and 82321