What is the Greatest Common Factor of 21238 and 21252?

Greatest common factor (GCF) of 21238 and 21252 is 14.

GCF(21238,21252) = 14

We will now calculate the prime factors of 21238 and 21252, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 21238 and 21252.

How to find the GCF of 21238 and 21252?

We will first find the prime factorization of 21238 and 21252. After we will calculate the factors of 21238 and 21252 and find the biggest common factor number .

Step-1: Prime Factorization of 21238

Prime factors of 21238 are 2, 7, 37, 41. Prime factorization of 21238 in exponential form is:

21238 = 2¹ × 7¹ × 37¹ × 41¹

Step-2: Prime Factorization of 21252

Prime factors of 21252 are 2, 3, 7, 11, 23. Prime factorization of 21252 in exponential form is:

21252 = 2² × 3¹ × 7¹ × 11¹ × 23¹

Step-3: Factors of 21238

List of positive integer factors of 21238 that divides 21238 without a remainder.

1, 2, 7, 14, 37, 41, 74, 82, 259, 287, 518, 574, 1517, 3034, 10619

Step-4: Factors of 21252

List of positive integer factors of 21252 that divides 21238 without a remainder.

1, 2, 3, 4, 6, 7, 11, 12, 14, 21, 22, 23, 28, 33, 42, 44, 46, 66, 69, 77, 84, 92, 132, 138, 154, 161, 231, 253, 276, 308, 322, 462, 483, 506, 644, 759, 924, 966, 1012, 1518, 1771, 1932, 3036, 3542, 5313, 7084, 10626

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 21238 and 21252. The biggest common factor number is the GCF number.
So the greatest common factor 21238 and 21252 is 14.

Also check out the Least Common Multiple of 21238 and 21252