What is the Greatest Common Factor of 21909 and 21917?

Greatest common factor (GCF) of 21909 and 21917 is 1.

GCF(21909,21917) = 1

We will now calculate the prime factors of 21909 and 21917, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 21909 and 21917.

How to find the GCF of 21909 and 21917?

We will first find the prime factorization of 21909 and 21917. After we will calculate the factors of 21909 and 21917 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 21917

Prime factors of 21917 are 7, 31, 101. Prime factorization of 21917 in exponential form is:

21917 = 7¹ × 31¹ × 101¹

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 21917

List of positive integer factors of 21917 that divides 21909 without a remainder.

1, 7, 31, 101, 217, 707, 3131

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 21909 and 21917. The biggest common factor number is the GCF number.
So the greatest common factor 21909 and 21917 is 1.

Also check out the Least Common Multiple of 21909 and 21917