What is the Greatest Common Factor of 82569 and 82584?

Greatest common factor (GCF) of 82569 and 82584 is 3.

GCF(82569,82584) = 3

We will now calculate the prime factors of 82569 and 82584, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 82569 and 82584.

How to find the GCF of 82569 and 82584?

We will first find the prime factorization of 82569 and 82584. After we will calculate the factors of 82569 and 82584 and find the biggest common factor number .

Step-1: Prime Factorization of 82569

Prime factors of 82569 are 3, 17, 1619. Prime factorization of 82569 in exponential form is:

82569 = 3¹ × 17¹ × 1619¹

Step-2: Prime Factorization of 82584

Prime factors of 82584 are 2, 3, 31, 37. Prime factorization of 82584 in exponential form is:

82584 = 2³ × 3² × 31¹ × 37¹

Step-3: Factors of 82569

List of positive integer factors of 82569 that divides 82569 without a remainder.

1, 3, 17, 51, 1619, 4857, 27523

Step-4: Factors of 82584

List of positive integer factors of 82584 that divides 82569 without a remainder.

1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 31, 36, 37, 62, 72, 74, 93, 111, 124, 148, 186, 222, 248, 279, 296, 333, 372, 444, 558, 666, 744, 888, 1116, 1147, 1332, 2232, 2294, 2664, 3441, 4588, 6882, 9176, 10323, 13764, 20646, 27528, 41292

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 82569 and 82584. The biggest common factor number is the GCF number.
So the greatest common factor 82569 and 82584 is 3.

Also check out the Least Common Multiple of 82569 and 82584