What is the Greatest Common Factor of 21824 and 21842?

Greatest common factor (GCF) of 21824 and 21842 is 2.

GCF(21824,21842) = 2

We will now calculate the prime factors of 21824 and 21842, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 21824 and 21842.

How to find the GCF of 21824 and 21842?

We will first find the prime factorization of 21824 and 21842. After we will calculate the factors of 21824 and 21842 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 21842

Prime factors of 21842 are 2, 67, 163. Prime factorization of 21842 in exponential form is:

21842 = 2¹ × 67¹ × 163¹

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 21842

List of positive integer factors of 21842 that divides 21824 without a remainder.

1, 2, 67, 134, 163, 326, 10921

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 21824 and 21842. The biggest common factor number is the GCF number.
So the greatest common factor 21824 and 21842 is 2.

Also check out the Least Common Multiple of 21824 and 21842