What is the Greatest Common Factor of 82289 and 82304?

Greatest common factor (GCF) of 82289 and 82304 is 1.

GCF(82289,82304) = 1

We will now calculate the prime factors of 82289 and 82304, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 82289 and 82304.

How to find the GCF of 82289 and 82304?

We will first find the prime factorization of 82289 and 82304. After we will calculate the factors of 82289 and 82304 and find the biggest common factor number .

Step-1: Prime Factorization of 82289

Prime factors of 82289 are 19, 61, 71. Prime factorization of 82289 in exponential form is:

82289 = 19¹ × 61¹ × 71¹

Step-2: Prime Factorization of 82304

Prime factors of 82304 are 2, 643. Prime factorization of 82304 in exponential form is:

82304 = 2⁷ × 643¹

Step-3: Factors of 82289

List of positive integer factors of 82289 that divides 82289 without a remainder.

1, 19, 61, 71, 1159, 1349, 4331

Step-4: Factors of 82304

List of positive integer factors of 82304 that divides 82289 without a remainder.

1, 2, 4, 8, 16, 32, 64, 128, 643, 1286, 2572, 5144, 10288, 20576, 41152

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 82289 and 82304. The biggest common factor number is the GCF number.
So the greatest common factor 82289 and 82304 is 1.

Also check out the Least Common Multiple of 82289 and 82304