What is the Greatest Common Factor of 21105 and 21109?

Greatest common factor (GCF) of 21105 and 21109 is 1.

GCF(21105,21109) = 1

We will now calculate the prime factors of 21105 and 21109, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 21105 and 21109.

How to find the GCF of 21105 and 21109?

We will first find the prime factorization of 21105 and 21109. After we will calculate the factors of 21105 and 21109 and find the biggest common factor number .

Step-1: Prime Factorization of 21105

Prime factors of 21105 are 3, 5, 7, 67. Prime factorization of 21105 in exponential form is:

21105 = 3² × 5¹ × 7¹ × 67¹

Step-2: Prime Factorization of 21109

Prime factors of 21109 are 11, 19, 101. Prime factorization of 21109 in exponential form is:

21109 = 11¹ × 19¹ × 101¹

Step-3: Factors of 21105

List of positive integer factors of 21105 that divides 21105 without a remainder.

1, 3, 5, 7, 9, 15, 21, 35, 45, 63, 67, 105, 201, 315, 335, 469, 603, 1005, 1407, 2345, 3015, 4221, 7035

Step-4: Factors of 21109

List of positive integer factors of 21109 that divides 21105 without a remainder.

1, 11, 19, 101, 209, 1111, 1919

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 21105 and 21109. The biggest common factor number is the GCF number.
So the greatest common factor 21105 and 21109 is 1.

Also check out the Least Common Multiple of 21105 and 21109