What is the Greatest Common Factor of 21856 and 21874?

Greatest common factor (GCF) of 21856 and 21874 is 2.

GCF(21856,21874) = 2

We will now calculate the prime factors of 21856 and 21874, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 21856 and 21874.

How to find the GCF of 21856 and 21874?

We will first find the prime factorization of 21856 and 21874. After we will calculate the factors of 21856 and 21874 and find the biggest common factor number .

Step-1: Prime Factorization of 21856

Prime factors of 21856 are 2, 683. Prime factorization of 21856 in exponential form is:

21856 = 2⁵ × 683¹

Step-2: Prime Factorization of 21874

Prime factors of 21874 are 2, 10937. Prime factorization of 21874 in exponential form is:

21874 = 2¹ × 10937¹

Step-3: Factors of 21856

List of positive integer factors of 21856 that divides 21856 without a remainder.

1, 2, 4, 8, 16, 32, 683, 1366, 2732, 5464, 10928

Step-4: Factors of 21874

List of positive integer factors of 21874 that divides 21856 without a remainder.

1, 2, 10937

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 21856 and 21874. The biggest common factor number is the GCF number.
So the greatest common factor 21856 and 21874 is 2.

Also check out the Least Common Multiple of 21856 and 21874