What is the Greatest Common Factor of 21805 and 21814?

Greatest common factor (GCF) of 21805 and 21814 is 1.

GCF(21805,21814) = 1

We will now calculate the prime factors of 21805 and 21814, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 21805 and 21814.

How to find the GCF of 21805 and 21814?

We will first find the prime factorization of 21805 and 21814. After we will calculate the factors of 21805 and 21814 and find the biggest common factor number .

Step-1: Prime Factorization of 21805

Prime factors of 21805 are 5, 7, 89. Prime factorization of 21805 in exponential form is:

21805 = 5¹ × 7² × 89¹

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 21805

List of positive integer factors of 21805 that divides 21805 without a remainder.

1, 5, 7, 35, 49, 89, 245, 445, 623, 3115, 4361

Step-4: Factors of 21814

List of positive integer factors of 21814 that divides 21805 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 21805 and 21814. The biggest common factor number is the GCF number.
So the greatest common factor 21805 and 21814 is 1.

Also check out the Least Common Multiple of 21805 and 21814