What is the Greatest Common Factor of 21838 and 21856?

Greatest common factor (GCF) of 21838 and 21856 is 2.

GCF(21838,21856) = 2

We will now calculate the prime factors of 21838 and 21856, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 21838 and 21856.

How to find the GCF of 21838 and 21856?

We will first find the prime factorization of 21838 and 21856. After we will calculate the factors of 21838 and 21856 and find the biggest common factor number .

Step-1: Prime Factorization of 21838

Prime factors of 21838 are 2, 61, 179. Prime factorization of 21838 in exponential form is:

21838 = 2¹ × 61¹ × 179¹

Step-2: Prime Factorization of 21856

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

21856 = 2⁵ × 683¹

Step-3: Factors of 21838

List of positive integer factors of 21838 that divides 21838 without a remainder.

1, 2, 61, 122, 179, 358, 10919

Step-4: Factors of 21856

List of positive integer factors of 21856 that divides 21838 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 21838 and 21856. The biggest common factor number is the GCF number.
So the greatest common factor 21838 and 21856 is 2.

Also check out the Least Common Multiple of 21838 and 21856