What is the Greatest Common Factor of 624 and 638?

Greatest common factor (GCF) of 624 and 638 is 2.

GCF(624,638) = 2

We will now calculate the prime factors of 624 and 638, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 624 and 638.

How to find the GCF of 624 and 638?

We will first find the prime factorization of 624 and 638. After we will calculate the factors of 624 and 638 and find the biggest common factor number .

Step-1: Prime Factorization of 624

Prime factors of 624 are 2, 3, 13. Prime factorization of 624 in exponential form is:

624 = 2⁴ × 3¹ × 13¹

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 624

List of positive integer factors of 624 that divides 624 without a remainder.

1, 2, 3, 4, 6, 8, 12, 13, 16, 24, 26, 39, 48, 52, 78, 104, 156, 208, 312

Step-4: Factors of 638

List of positive integer factors of 638 that divides 624 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 624 and 638. The biggest common factor number is the GCF number.
So the greatest common factor 624 and 638 is 2.

Also check out the Least Common Multiple of 624 and 638