What is the Greatest Common Factor of 82289 and 82300?

Greatest common factor (GCF) of 82289 and 82300 is 1.

GCF(82289,82300) = 1

We will now calculate the prime factors of 82289 and 82300, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 82289 and 82300.

How to find the GCF of 82289 and 82300?

We will first find the prime factorization of 82289 and 82300. After we will calculate the factors of 82289 and 82300 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 82300

Prime factors of 82300 are 2, 5, 823. Prime factorization of 82300 in exponential form is:

82300 = 2² × 5² × 823¹

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 82300

List of positive integer factors of 82300 that divides 82289 without a remainder.

1, 2, 4, 5, 10, 20, 25, 50, 100, 823, 1646, 3292, 4115, 8230, 16460, 20575, 41150

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 82289 and 82300. The biggest common factor number is the GCF number.
So the greatest common factor 82289 and 82300 is 1.

Also check out the Least Common Multiple of 82289 and 82300