What is the Greatest Common Factor of 21538 and 21549?

Greatest common factor (GCF) of 21538 and 21549 is 11.

GCF(21538,21549) = 11

We will now calculate the prime factors of 21538 and 21549, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 21538 and 21549.

How to find the GCF of 21538 and 21549?

We will first find the prime factorization of 21538 and 21549. After we will calculate the factors of 21538 and 21549 and find the biggest common factor number .

Step-1: Prime Factorization of 21538

Prime factors of 21538 are 2, 11, 89. Prime factorization of 21538 in exponential form is:

21538 = 2¹ × 11² × 89¹

Step-2: Prime Factorization of 21549

Prime factors of 21549 are 3, 11, 653. Prime factorization of 21549 in exponential form is:

21549 = 3¹ × 11¹ × 653¹

Step-3: Factors of 21538

List of positive integer factors of 21538 that divides 21538 without a remainder.

1, 2, 11, 22, 89, 121, 178, 242, 979, 1958, 10769

Step-4: Factors of 21549

List of positive integer factors of 21549 that divides 21538 without a remainder.

1, 3, 11, 33, 653, 1959, 7183

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 21538 and 21549. The biggest common factor number is the GCF number.
So the greatest common factor 21538 and 21549 is 11.

Also check out the Least Common Multiple of 21538 and 21549