What is the Greatest Common Factor of 82569 and 82586?

Greatest common factor (GCF) of 82569 and 82586 is 17.

GCF(82569,82586) = 17

We will now calculate the prime factors of 82569 and 82586, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 82569 and 82586.

How to find the GCF of 82569 and 82586?

We will first find the prime factorization of 82569 and 82586. After we will calculate the factors of 82569 and 82586 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 82586

Prime factors of 82586 are 2, 7, 17, 347. Prime factorization of 82586 in exponential form is:

82586 = 2¹ × 7¹ × 17¹ × 347¹

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 82586

List of positive integer factors of 82586 that divides 82569 without a remainder.

1, 2, 7, 14, 17, 34, 119, 238, 347, 694, 2429, 4858, 5899, 11798, 41293

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 82569 and 82586. The biggest common factor number is the GCF number.
So the greatest common factor 82569 and 82586 is 17.

Also check out the Least Common Multiple of 82569 and 82586