What is the Greatest Common Factor of 21904 and 21909?

Greatest common factor (GCF) of 21904 and 21909 is 1.

GCF(21904,21909) = 1

We will now calculate the prime factors of 21904 and 21909, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 21904 and 21909.

How to find the GCF of 21904 and 21909?

We will first find the prime factorization of 21904 and 21909. After we will calculate the factors of 21904 and 21909 and find the biggest common factor number .

Step-1: Prime Factorization of 21904

Prime factors of 21904 are 2, 37. Prime factorization of 21904 in exponential form is:

21904 = 2⁴ × 37²

Step-2: 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-3: Factors of 21904

List of positive integer factors of 21904 that divides 21904 without a remainder.

1, 2, 4, 8, 16, 37, 74, 148, 296, 592, 1369, 2738, 5476, 10952

Step-4: Factors of 21909

List of positive integer factors of 21909 that divides 21904 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 21904 and 21909. The biggest common factor number is the GCF number.
So the greatest common factor 21904 and 21909 is 1.

Also check out the Least Common Multiple of 21904 and 21909