What is the Greatest Common Factor of 21936 and 21952?

Greatest common factor (GCF) of 21936 and 21952 is 16.

GCF(21936,21952) = 16

We will now calculate the prime factors of 21936 and 21952, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 21936 and 21952.

How to find the GCF of 21936 and 21952?

We will first find the prime factorization of 21936 and 21952. After we will calculate the factors of 21936 and 21952 and find the biggest common factor number .

Step-1: Prime Factorization of 21936

Prime factors of 21936 are 2, 3, 457. Prime factorization of 21936 in exponential form is:

21936 = 2⁴ × 3¹ × 457¹

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 21936

List of positive integer factors of 21936 that divides 21936 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 24, 48, 457, 914, 1371, 1828, 2742, 3656, 5484, 7312, 10968

Step-4: Factors of 21952

List of positive integer factors of 21952 that divides 21936 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 21936 and 21952. The biggest common factor number is the GCF number.
So the greatest common factor 21936 and 21952 is 16.

Also check out the Least Common Multiple of 21936 and 21952