What is the Greatest Common Factor of 82297 and 82314?

Greatest common factor (GCF) of 82297 and 82314 is 17.

GCF(82297,82314) = 17

We will now calculate the prime factors of 82297 and 82314, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 82297 and 82314.

How to find the GCF of 82297 and 82314?

We will first find the prime factorization of 82297 and 82314. After we will calculate the factors of 82297 and 82314 and find the biggest common factor number .

Step-1: Prime Factorization of 82297

Prime factors of 82297 are 17, 47, 103. Prime factorization of 82297 in exponential form is:

82297 = 17¹ × 47¹ × 103¹

Step-2: 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-3: Factors of 82297

List of positive integer factors of 82297 that divides 82297 without a remainder.

1, 17, 47, 103, 799, 1751, 4841

Step-4: Factors of 82314

List of positive integer factors of 82314 that divides 82297 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 82297 and 82314. The biggest common factor number is the GCF number.
So the greatest common factor 82297 and 82314 is 17.

Also check out the Least Common Multiple of 82297 and 82314