What is the Greatest Common Factor of 21824 and 21836?

Greatest common factor (GCF) of 21824 and 21836 is 4.

GCF(21824,21836) = 4

We will now calculate the prime factors of 21824 and 21836, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 21824 and 21836.

How to find the GCF of 21824 and 21836?

We will first find the prime factorization of 21824 and 21836. After we will calculate the factors of 21824 and 21836 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 21836

Prime factors of 21836 are 2, 53, 103. Prime factorization of 21836 in exponential form is:

21836 = 2² × 53¹ × 103¹

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 21836

List of positive integer factors of 21836 that divides 21824 without a remainder.

1, 2, 4, 53, 103, 106, 206, 212, 412, 5459, 10918

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 21824 and 21836. The biggest common factor number is the GCF number.
So the greatest common factor 21824 and 21836 is 4.

Also check out the Least Common Multiple of 21824 and 21836