What is the Greatest Common Factor of 21638 and 21649?

Greatest common factor (GCF) of 21638 and 21649 is 1.

GCF(21638,21649) = 1

We will now calculate the prime factors of 21638 and 21649, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 21638 and 21649.

How to find the GCF of 21638 and 21649?

We will first find the prime factorization of 21638 and 21649. After we will calculate the factors of 21638 and 21649 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 21649

Prime factors of 21649 are 21649. Prime factorization of 21649 in exponential form is:

21649 = 21649¹

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 21649

List of positive integer factors of 21649 that divides 21638 without a remainder.

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 21638 and 21649. The biggest common factor number is the GCF number.
So the greatest common factor 21638 and 21649 is 1.

Also check out the Least Common Multiple of 21638 and 21649