What is the Greatest Common Factor of 10586 and 10600?

Greatest common factor (GCF) of 10586 and 10600 is 2.

GCF(10586,10600) = 2

We will now calculate the prime factors of 10586 and 10600, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 10586 and 10600.

How to find the GCF of 10586 and 10600?

We will first find the prime factorization of 10586 and 10600. After we will calculate the factors of 10586 and 10600 and find the biggest common factor number .

Step-1: Prime Factorization of 10586

Prime factors of 10586 are 2, 67, 79. Prime factorization of 10586 in exponential form is:

10586 = 2¹ × 67¹ × 79¹

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 10586

List of positive integer factors of 10586 that divides 10586 without a remainder.

1, 2, 67, 79, 134, 158, 5293

Step-4: Factors of 10600

List of positive integer factors of 10600 that divides 10586 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 10586 and 10600. The biggest common factor number is the GCF number.
So the greatest common factor 10586 and 10600 is 2.

Also check out the Least Common Multiple of 10586 and 10600