What is the Greatest Common Factor of 21808 and 21822?

Greatest common factor (GCF) of 21808 and 21822 is 2.

GCF(21808,21822) = 2

We will now calculate the prime factors of 21808 and 21822, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 21808 and 21822.

How to find the GCF of 21808 and 21822?

We will first find the prime factorization of 21808 and 21822. After we will calculate the factors of 21808 and 21822 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 21822

Prime factors of 21822 are 2, 3, 3637. Prime factorization of 21822 in exponential form is:

21822 = 2¹ × 3¹ × 3637¹

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 21822

List of positive integer factors of 21822 that divides 21808 without a remainder.

1, 2, 3, 6, 3637, 7274, 10911

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 21808 and 21822. The biggest common factor number is the GCF number.
So the greatest common factor 21808 and 21822 is 2.

Also check out the Least Common Multiple of 21808 and 21822