What is the Greatest Common Factor of 21824 and 21838?

Greatest common factor (GCF) of 21824 and 21838 is 2.

GCF(21824,21838) = 2

We will now calculate the prime factors of 21824 and 21838, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 21824 and 21838.

How to find the GCF of 21824 and 21838?

We will first find the prime factorization of 21824 and 21838. After we will calculate the factors of 21824 and 21838 and find the biggest common factor number .

Step-1: Prime Factorization of 21824

Prime factors of 21824 are 2, 11, 31. Prime factorization of 21824 in exponential form is:

21824 = 2⁶ × 11¹ × 31¹

Step-2: 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-3: Factors of 21824

List of positive integer factors of 21824 that divides 21824 without a remainder.

1, 2, 4, 8, 11, 16, 22, 31, 32, 44, 62, 64, 88, 124, 176, 248, 341, 352, 496, 682, 704, 992, 1364, 1984, 2728, 5456, 10912

Step-4: Factors of 21838

List of positive integer factors of 21838 that divides 21824 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 21824 and 21838. The biggest common factor number is the GCF number.
So the greatest common factor 21824 and 21838 is 2.

Also check out the Least Common Multiple of 21824 and 21838