What is the Greatest Common Factor of 10582 and 10600?

Greatest common factor (GCF) of 10582 and 10600 is 2.

GCF(10582,10600) = 2

We will now calculate the prime factors of 10582 and 10600, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 10582 and 10600.

How to find the GCF of 10582 and 10600?

We will first find the prime factorization of 10582 and 10600. After we will calculate the factors of 10582 and 10600 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 10600

Prime factors of 10600 are 2, 5, 53. Prime factorization of 10600 in exponential form is:

10600 = 2³ × 5² × 53¹

Step-3: Factors of 10582

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

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

Step-4: Factors of 10600

List of positive integer factors of 10600 that divides 10582 without a remainder.

1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 53, 100, 106, 200, 212, 265, 424, 530, 1060, 1325, 2120, 2650, 5300

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 10582 and 10600. The biggest common factor number is the GCF number.
So the greatest common factor 10582 and 10600 is 2.

Also check out the Least Common Multiple of 10582 and 10600