What is the Greatest Common Factor of 638 and 649?

Greatest common factor (GCF) of 638 and 649 is 11.

GCF(638,649) = 11

We will now calculate the prime factors of 638 and 649, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 638 and 649.

How to find the GCF of 638 and 649?

We will first find the prime factorization of 638 and 649. After we will calculate the factors of 638 and 649 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 649

Prime factors of 649 are 11, 59. Prime factorization of 649 in exponential form is:

649 = 11¹ × 59¹

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 649

List of positive integer factors of 649 that divides 638 without a remainder.

1, 11, 59

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 638 and 649. The biggest common factor number is the GCF number.
So the greatest common factor 638 and 649 is 11.

Also check out the Least Common Multiple of 638 and 649