What is the Greatest Common Factor of 21920 and 21936?

Greatest common factor (GCF) of 21920 and 21936 is 16.

GCF(21920,21936) = 16

We will now calculate the prime factors of 21920 and 21936, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 21920 and 21936.

How to find the GCF of 21920 and 21936?

We will first find the prime factorization of 21920 and 21936. After we will calculate the factors of 21920 and 21936 and find the biggest common factor number .

Step-1: Prime Factorization of 21920

Prime factors of 21920 are 2, 5, 137. Prime factorization of 21920 in exponential form is:

21920 = 2⁵ × 5¹ × 137¹

Step-2: 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-3: Factors of 21920

List of positive integer factors of 21920 that divides 21920 without a remainder.

1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 80, 137, 160, 274, 548, 685, 1096, 1370, 2192, 2740, 4384, 5480, 10960

Step-4: Factors of 21936

List of positive integer factors of 21936 that divides 21920 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 21920 and 21936. The biggest common factor number is the GCF number.
So the greatest common factor 21920 and 21936 is 16.

Also check out the Least Common Multiple of 21920 and 21936