What is the Greatest Common Factor of 21538 and 21554?

Greatest common factor (GCF) of 21538 and 21554 is 2.

GCF(21538,21554) = 2

We will now calculate the prime factors of 21538 and 21554, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 21538 and 21554.

How to find the GCF of 21538 and 21554?

We will first find the prime factorization of 21538 and 21554. After we will calculate the factors of 21538 and 21554 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 21554

Prime factors of 21554 are 2, 13, 829. Prime factorization of 21554 in exponential form is:

21554 = 2¹ × 13¹ × 829¹

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 21554

List of positive integer factors of 21554 that divides 21538 without a remainder.

1, 2, 13, 26, 829, 1658, 10777

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 21538 and 21554. The biggest common factor number is the GCF number.
So the greatest common factor 21538 and 21554 is 2.

Also check out the Least Common Multiple of 21538 and 21554