What is the Greatest Common Factor of 21808 and 21828?

Greatest common factor (GCF) of 21808 and 21828 is 4.

GCF(21808,21828) = 4

We will now calculate the prime factors of 21808 and 21828, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 21808 and 21828.

How to find the GCF of 21808 and 21828?

We will first find the prime factorization of 21808 and 21828. After we will calculate the factors of 21808 and 21828 and find the biggest common factor number .

Step-1: Prime Factorization of 21808

Prime factors of 21808 are 2, 29, 47. Prime factorization of 21808 in exponential form is:

21808 = 2⁴ × 29¹ × 47¹

Step-2: Prime Factorization of 21828

Prime factors of 21828 are 2, 3, 17, 107. Prime factorization of 21828 in exponential form is:

21828 = 2² × 3¹ × 17¹ × 107¹

Step-3: Factors of 21808

List of positive integer factors of 21808 that divides 21808 without a remainder.

1, 2, 4, 8, 16, 29, 47, 58, 94, 116, 188, 232, 376, 464, 752, 1363, 2726, 5452, 10904

Step-4: Factors of 21828

List of positive integer factors of 21828 that divides 21808 without a remainder.

1, 2, 3, 4, 6, 12, 17, 34, 51, 68, 102, 107, 204, 214, 321, 428, 642, 1284, 1819, 3638, 5457, 7276, 10914

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 21808 and 21828. The biggest common factor number is the GCF number.
So the greatest common factor 21808 and 21828 is 4.

Also check out the Least Common Multiple of 21808 and 21828