What is the Greatest Common Factor of 82365 and 82382?

Greatest common factor (GCF) of 82365 and 82382 is 17.

GCF(82365,82382) = 17

We will now calculate the prime factors of 82365 and 82382, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 82365 and 82382.

How to find the GCF of 82365 and 82382?

We will first find the prime factorization of 82365 and 82382. After we will calculate the factors of 82365 and 82382 and find the biggest common factor number .

Step-1: Prime Factorization of 82365

Prime factors of 82365 are 3, 5, 17, 19. Prime factorization of 82365 in exponential form is:

82365 = 3¹ × 5¹ × 17² × 19¹

Step-2: Prime Factorization of 82382

Prime factors of 82382 are 2, 17, 2423. Prime factorization of 82382 in exponential form is:

82382 = 2¹ × 17¹ × 2423¹

Step-3: Factors of 82365

List of positive integer factors of 82365 that divides 82365 without a remainder.

1, 3, 5, 15, 17, 19, 51, 57, 85, 95, 255, 285, 289, 323, 867, 969, 1445, 1615, 4335, 4845, 5491, 16473, 27455

Step-4: Factors of 82382

List of positive integer factors of 82382 that divides 82365 without a remainder.

1, 2, 17, 34, 2423, 4846, 41191

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 82365 and 82382. The biggest common factor number is the GCF number.
So the greatest common factor 82365 and 82382 is 17.

Also check out the Least Common Multiple of 82365 and 82382