What is the Greatest Common Factor of 21638 and 21656?

Greatest common factor (GCF) of 21638 and 21656 is 2.

GCF(21638,21656) = 2

We will now calculate the prime factors of 21638 and 21656, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 21638 and 21656.

How to find the GCF of 21638 and 21656?

We will first find the prime factorization of 21638 and 21656. After we will calculate the factors of 21638 and 21656 and find the biggest common factor number .

Step-1: Prime Factorization of 21638

Prime factors of 21638 are 2, 31, 349. Prime factorization of 21638 in exponential form is:

21638 = 2¹ × 31¹ × 349¹

Step-2: Prime Factorization of 21656

Prime factors of 21656 are 2, 2707. Prime factorization of 21656 in exponential form is:

21656 = 2³ × 2707¹

Step-3: Factors of 21638

List of positive integer factors of 21638 that divides 21638 without a remainder.

1, 2, 31, 62, 349, 698, 10819

Step-4: Factors of 21656

List of positive integer factors of 21656 that divides 21638 without a remainder.

1, 2, 4, 8, 2707, 5414, 10828

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 21638 and 21656. The biggest common factor number is the GCF number.
So the greatest common factor 21638 and 21656 is 2.

Also check out the Least Common Multiple of 21638 and 21656