What is the Greatest Common Factor of 627 and 638?

Greatest common factor (GCF) of 627 and 638 is 11.

GCF(627,638) = 11

We will now calculate the prime factors of 627 and 638, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 627 and 638.

How to find the GCF of 627 and 638?

We will first find the prime factorization of 627 and 638. After we will calculate the factors of 627 and 638 and find the biggest common factor number .

Step-1: Prime Factorization of 627

Prime factors of 627 are 3, 11, 19. Prime factorization of 627 in exponential form is:

627 = 3¹ × 11¹ × 19¹

Step-2: Prime Factorization of 638

Prime factors of 638 are 2, 11, 29. Prime factorization of 638 in exponential form is:

638 = 2¹ × 11¹ × 29¹

Step-3: Factors of 627

List of positive integer factors of 627 that divides 627 without a remainder.

1, 3, 11, 19, 33, 57, 209

Step-4: Factors of 638

List of positive integer factors of 638 that divides 627 without a remainder.

1, 2, 11, 22, 29, 58, 319

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 627 and 638. The biggest common factor number is the GCF number.
So the greatest common factor 627 and 638 is 11.

Also check out the Least Common Multiple of 627 and 638