What is the Greatest Common Factor of 21800 and 21814?

Greatest common factor (GCF) of 21800 and 21814 is 2.

GCF(21800,21814) = 2

We will now calculate the prime factors of 21800 and 21814, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 21800 and 21814.

How to find the GCF of 21800 and 21814?

We will first find the prime factorization of 21800 and 21814. After we will calculate the factors of 21800 and 21814 and find the biggest common factor number .

Step-1: Prime Factorization of 21800

Prime factors of 21800 are 2, 5, 109. Prime factorization of 21800 in exponential form is:

21800 = 2³ × 5² × 109¹

Step-2: Prime Factorization of 21814

Prime factors of 21814 are 2, 13, 839. Prime factorization of 21814 in exponential form is:

21814 = 2¹ × 13¹ × 839¹

Step-3: Factors of 21800

List of positive integer factors of 21800 that divides 21800 without a remainder.

1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 109, 200, 218, 436, 545, 872, 1090, 2180, 2725, 4360, 5450, 10900

Step-4: Factors of 21814

List of positive integer factors of 21814 that divides 21800 without a remainder.

1, 2, 13, 26, 839, 1678, 10907

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 21800 and 21814. The biggest common factor number is the GCF number.
So the greatest common factor 21800 and 21814 is 2.

Also check out the Least Common Multiple of 21800 and 21814