What is the Greatest Common Factor of 2586 and 2600?

Greatest common factor (GCF) of 2586 and 2600 is 2.

GCF(2586,2600) = 2

We will now calculate the prime factors of 2586 and 2600, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 2586 and 2600.

How to find the GCF of 2586 and 2600?

We will first find the prime factorization of 2586 and 2600. After we will calculate the factors of 2586 and 2600 and find the biggest common factor number .

Step-1: Prime Factorization of 2586

Prime factors of 2586 are 2, 3, 431. Prime factorization of 2586 in exponential form is:

2586 = 2¹ × 3¹ × 431¹

Step-2: Prime Factorization of 2600

Prime factors of 2600 are 2, 5, 13. Prime factorization of 2600 in exponential form is:

2600 = 2³ × 5² × 13¹

Step-3: Factors of 2586

List of positive integer factors of 2586 that divides 2586 without a remainder.

1, 2, 3, 6, 431, 862, 1293

Step-4: Factors of 2600

List of positive integer factors of 2600 that divides 2586 without a remainder.

1, 2, 4, 5, 8, 10, 13, 20, 25, 26, 40, 50, 52, 65, 100, 104, 130, 200, 260, 325, 520, 650, 1300

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 2586 and 2600. The biggest common factor number is the GCF number.
So the greatest common factor 2586 and 2600 is 2.

Also check out the Least Common Multiple of 2586 and 2600