What is the Greatest Common Factor of 638 and 652?

Greatest common factor (GCF) of 638 and 652 is 2.

GCF(638,652) = 2

We will now calculate the prime factors of 638 and 652, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 638 and 652.

How to find the GCF of 638 and 652?

We will first find the prime factorization of 638 and 652. After we will calculate the factors of 638 and 652 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 652

Prime factors of 652 are 2, 163. Prime factorization of 652 in exponential form is:

652 = 2² × 163¹

Step-3: Factors of 638

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

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

Step-4: Factors of 652

List of positive integer factors of 652 that divides 638 without a remainder.

1, 2, 4, 163, 326

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 638 and 652. The biggest common factor number is the GCF number.
So the greatest common factor 638 and 652 is 2.

Also check out the Least Common Multiple of 638 and 652