What is the Greatest Common Factor of 21812 and 21824?

Greatest common factor (GCF) of 21812 and 21824 is 4.

GCF(21812,21824) = 4

We will now calculate the prime factors of 21812 and 21824, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 21812 and 21824.

How to find the GCF of 21812 and 21824?

We will first find the prime factorization of 21812 and 21824. After we will calculate the factors of 21812 and 21824 and find the biggest common factor number .

Step-1: Prime Factorization of 21812

Prime factors of 21812 are 2, 7, 19, 41. Prime factorization of 21812 in exponential form is:

21812 = 2² × 7¹ × 19¹ × 41¹

Step-2: 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-3: Factors of 21812

List of positive integer factors of 21812 that divides 21812 without a remainder.

1, 2, 4, 7, 14, 19, 28, 38, 41, 76, 82, 133, 164, 266, 287, 532, 574, 779, 1148, 1558, 3116, 5453, 10906

Step-4: Factors of 21824

List of positive integer factors of 21824 that divides 21812 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 21812 and 21824. The biggest common factor number is the GCF number.
So the greatest common factor 21812 and 21824 is 4.

Also check out the Least Common Multiple of 21812 and 21824