What is the Greatest Common Factor of 21538 and 21546?

Greatest common factor (GCF) of 21538 and 21546 is 2.

GCF(21538,21546) = 2

We will now calculate the prime factors of 21538 and 21546, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 21538 and 21546.

How to find the GCF of 21538 and 21546?

We will first find the prime factorization of 21538 and 21546. After we will calculate the factors of 21538 and 21546 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 21546

Prime factors of 21546 are 2, 3, 7, 19. Prime factorization of 21546 in exponential form is:

21546 = 2¹ × 3⁴ × 7¹ × 19¹

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 21546

List of positive integer factors of 21546 that divides 21538 without a remainder.

1, 2, 3, 6, 7, 9, 14, 18, 19, 21, 27, 38, 42, 54, 57, 63, 81, 114, 126, 133, 162, 171, 189, 266, 342, 378, 399, 513, 567, 798, 1026, 1134, 1197, 1539, 2394, 3078, 3591, 7182, 10773

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 21538 and 21546. The biggest common factor number is the GCF number.
So the greatest common factor 21538 and 21546 is 2.

Also check out the Least Common Multiple of 21538 and 21546