What is the Greatest Common Factor of 21938 and 21952?

Greatest common factor (GCF) of 21938 and 21952 is 14.

GCF(21938,21952) = 14

We will now calculate the prime factors of 21938 and 21952, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 21938 and 21952.

How to find the GCF of 21938 and 21952?

We will first find the prime factorization of 21938 and 21952. After we will calculate the factors of 21938 and 21952 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 21952

Prime factors of 21952 are 2, 7. Prime factorization of 21952 in exponential form is:

21952 = 2⁶ × 7³

Step-3: Factors of 21938

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

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

Step-4: Factors of 21952

List of positive integer factors of 21952 that divides 21938 without a remainder.

1, 2, 4, 7, 8, 14, 16, 28, 32, 49, 56, 64, 98, 112, 196, 224, 343, 392, 448, 686, 784, 1372, 1568, 2744, 3136, 5488, 10976

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 21938 and 21952. The biggest common factor number is the GCF number.
So the greatest common factor 21938 and 21952 is 14.

Also check out the Least Common Multiple of 21938 and 21952