What is the Greatest Common Factor of 10574 and 10582?

Greatest common factor (GCF) of 10574 and 10582 is 2.

GCF(10574,10582) = 2

We will now calculate the prime factors of 10574 and 10582, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 10574 and 10582.

How to find the GCF of 10574 and 10582?

We will first find the prime factorization of 10574 and 10582. After we will calculate the factors of 10574 and 10582 and find the biggest common factor number .

Step-1: Prime Factorization of 10574

Prime factors of 10574 are 2, 17, 311. Prime factorization of 10574 in exponential form is:

10574 = 2¹ × 17¹ × 311¹

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 10574

List of positive integer factors of 10574 that divides 10574 without a remainder.

1, 2, 17, 34, 311, 622, 5287

Step-4: Factors of 10582

List of positive integer factors of 10582 that divides 10574 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 10574 and 10582. The biggest common factor number is the GCF number.
So the greatest common factor 10574 and 10582 is 2.

Also check out the Least Common Multiple of 10574 and 10582