What is the Greatest Common Factor of 2538 and 2556?

Greatest common factor (GCF) of 2538 and 2556 is 18.

GCF(2538,2556) = 18

We will now calculate the prime factors of 2538 and 2556, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 2538 and 2556.

How to find the GCF of 2538 and 2556?

We will first find the prime factorization of 2538 and 2556. After we will calculate the factors of 2538 and 2556 and find the biggest common factor number .

Step-1: Prime Factorization of 2538

Prime factors of 2538 are 2, 3, 47. Prime factorization of 2538 in exponential form is:

2538 = 2¹ × 3³ × 47¹

Step-2: Prime Factorization of 2556

Prime factors of 2556 are 2, 3, 71. Prime factorization of 2556 in exponential form is:

2556 = 2² × 3² × 71¹

Step-3: Factors of 2538

List of positive integer factors of 2538 that divides 2538 without a remainder.

1, 2, 3, 6, 9, 18, 27, 47, 54, 94, 141, 282, 423, 846, 1269

Step-4: Factors of 2556

List of positive integer factors of 2556 that divides 2538 without a remainder.

1, 2, 3, 4, 6, 9, 12, 18, 36, 71, 142, 213, 284, 426, 639, 852, 1278

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 2538 and 2556. The biggest common factor number is the GCF number.
So the greatest common factor 2538 and 2556 is 18.

Also check out the Least Common Multiple of 2538 and 2556