What is the Greatest Common Factor of 21924 and 21938?

Greatest common factor (GCF) of 21924 and 21938 is 14.

GCF(21924,21938) = 14

We will now calculate the prime factors of 21924 and 21938, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 21924 and 21938.

How to find the GCF of 21924 and 21938?

We will first find the prime factorization of 21924 and 21938. After we will calculate the factors of 21924 and 21938 and find the biggest common factor number .

Step-1: Prime Factorization of 21924

Prime factors of 21924 are 2, 3, 7, 29. Prime factorization of 21924 in exponential form is:

21924 = 2² × 3³ × 7¹ × 29¹

Step-2: Prime Factorization of 21938

Prime factors of 21938 are 2, 7, 1567. Prime factorization of 21938 in exponential form is:

21938 = 2¹ × 7¹ × 1567¹

Step-3: Factors of 21924

List of positive integer factors of 21924 that divides 21924 without a remainder.

1, 2, 3, 4, 6, 7, 9, 12, 14, 18, 21, 27, 28, 29, 36, 42, 54, 58, 63, 84, 87, 108, 116, 126, 174, 189, 203, 252, 261, 348, 378, 406, 522, 609, 756, 783, 812, 1044, 1218, 1566, 1827, 2436, 3132, 3654, 5481, 7308, 10962

Step-4: Factors of 21938

List of positive integer factors of 21938 that divides 21924 without a remainder.

1, 2, 7, 14, 1567, 3134, 10969

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 21924 and 21938. The biggest common factor number is the GCF number.
So the greatest common factor 21924 and 21938 is 14.

Also check out the Least Common Multiple of 21924 and 21938