What is the Greatest Common Factor of 1238 and 1254?

Greatest common factor (GCF) of 1238 and 1254 is 2.

GCF(1238,1254) = 2

We will now calculate the prime factors of 1238 and 1254, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1238 and 1254.

How to find the GCF of 1238 and 1254?

We will first find the prime factorization of 1238 and 1254. After we will calculate the factors of 1238 and 1254 and find the biggest common factor number .

Step-1: Prime Factorization of 1238

Prime factors of 1238 are 2, 619. Prime factorization of 1238 in exponential form is:

1238 = 2¹ × 619¹

Step-2: Prime Factorization of 1254

Prime factors of 1254 are 2, 3, 11, 19. Prime factorization of 1254 in exponential form is:

1254 = 2¹ × 3¹ × 11¹ × 19¹

Step-3: Factors of 1238

List of positive integer factors of 1238 that divides 1238 without a remainder.

1, 2, 619

Step-4: Factors of 1254

List of positive integer factors of 1254 that divides 1238 without a remainder.

1, 2, 3, 6, 11, 19, 22, 33, 38, 57, 66, 114, 209, 418, 627

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1238 and 1254. The biggest common factor number is the GCF number.
So the greatest common factor 1238 and 1254 is 2.

Also check out the Least Common Multiple of 1238 and 1254