What is the Greatest Common Factor of 21909 and 21918?

Greatest common factor (GCF) of 21909 and 21918 is 3.

GCF(21909,21918) = 3

We will now calculate the prime factors of 21909 and 21918, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 21909 and 21918.

How to find the GCF of 21909 and 21918?

We will first find the prime factorization of 21909 and 21918. After we will calculate the factors of 21909 and 21918 and find the biggest common factor number .

Step-1: Prime Factorization of 21909

Prime factors of 21909 are 3, 67, 109. Prime factorization of 21909 in exponential form is:

21909 = 3¹ × 67¹ × 109¹

Step-2: Prime Factorization of 21918

Prime factors of 21918 are 2, 3, 13, 281. Prime factorization of 21918 in exponential form is:

21918 = 2¹ × 3¹ × 13¹ × 281¹

Step-3: Factors of 21909

List of positive integer factors of 21909 that divides 21909 without a remainder.

1, 3, 67, 109, 201, 327, 7303

Step-4: Factors of 21918

List of positive integer factors of 21918 that divides 21909 without a remainder.

1, 2, 3, 6, 13, 26, 39, 78, 281, 562, 843, 1686, 3653, 7306, 10959

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 21909 and 21918. The biggest common factor number is the GCF number.
So the greatest common factor 21909 and 21918 is 3.

Also check out the Least Common Multiple of 21909 and 21918