What is the Greatest Common Factor of 82305 and 82317?

Greatest common factor (GCF) of 82305 and 82317 is 3.

GCF(82305,82317) = 3

We will now calculate the prime factors of 82305 and 82317, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 82305 and 82317.

How to find the GCF of 82305 and 82317?

We will first find the prime factorization of 82305 and 82317. After we will calculate the factors of 82305 and 82317 and find the biggest common factor number .

Step-1: Prime Factorization of 82305

Prime factors of 82305 are 3, 5, 31, 59. Prime factorization of 82305 in exponential form is:

82305 = 3² × 5¹ × 31¹ × 59¹

Step-2: Prime Factorization of 82317

Prime factors of 82317 are 3, 23, 1193. Prime factorization of 82317 in exponential form is:

82317 = 3¹ × 23¹ × 1193¹

Step-3: Factors of 82305

List of positive integer factors of 82305 that divides 82305 without a remainder.

1, 3, 5, 9, 15, 31, 45, 59, 93, 155, 177, 279, 295, 465, 531, 885, 1395, 1829, 2655, 5487, 9145, 16461, 27435

Step-4: Factors of 82317

List of positive integer factors of 82317 that divides 82305 without a remainder.

1, 3, 23, 69, 1193, 3579, 27439

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 82305 and 82317. The biggest common factor number is the GCF number.
So the greatest common factor 82305 and 82317 is 3.

Also check out the Least Common Multiple of 82305 and 82317