What is the Greatest Common Factor of 21909 and 21920?

Greatest common factor (GCF) of 21909 and 21920 is 1.

GCF(21909,21920) = 1

We will now calculate the prime factors of 21909 and 21920, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 21909 and 21920.

How to find the GCF of 21909 and 21920?

We will first find the prime factorization of 21909 and 21920. After we will calculate the factors of 21909 and 21920 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 21920

Prime factors of 21920 are 2, 5, 137. Prime factorization of 21920 in exponential form is:

21920 = 2⁵ × 5¹ × 137¹

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 21920

List of positive integer factors of 21920 that divides 21909 without a remainder.

1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 80, 137, 160, 274, 548, 685, 1096, 1370, 2192, 2740, 4384, 5480, 10960

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 21909 and 21920. The biggest common factor number is the GCF number.
So the greatest common factor 21909 and 21920 is 1.

Also check out the Least Common Multiple of 21909 and 21920