What is the Greatest Common Factor of 10569 and 10582?

Greatest common factor (GCF) of 10569 and 10582 is 13.

GCF(10569,10582) = 13

We will now calculate the prime factors of 10569 and 10582, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 10569 and 10582.

How to find the GCF of 10569 and 10582?

We will first find the prime factorization of 10569 and 10582. After we will calculate the factors of 10569 and 10582 and find the biggest common factor number .

Step-1: Prime Factorization of 10569

Prime factors of 10569 are 3, 13, 271. Prime factorization of 10569 in exponential form is:

10569 = 3¹ × 13¹ × 271¹

Step-2: Prime Factorization of 10582

Prime factors of 10582 are 2, 11, 13, 37. Prime factorization of 10582 in exponential form is:

10582 = 2¹ × 11¹ × 13¹ × 37¹

Step-3: Factors of 10569

List of positive integer factors of 10569 that divides 10569 without a remainder.

1, 3, 13, 39, 271, 813, 3523

Step-4: Factors of 10582

List of positive integer factors of 10582 that divides 10569 without a remainder.

1, 2, 11, 13, 22, 26, 37, 74, 143, 286, 407, 481, 814, 962, 5291

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 10569 and 10582. The biggest common factor number is the GCF number.
So the greatest common factor 10569 and 10582 is 13.

Also check out the Least Common Multiple of 10569 and 10582