What is the Greatest Common Factor of 21294 and 21309?

Greatest common factor (GCF) of 21294 and 21309 is 3.

GCF(21294,21309) = 3

We will now calculate the prime factors of 21294 and 21309, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 21294 and 21309.

How to find the GCF of 21294 and 21309?

We will first find the prime factorization of 21294 and 21309. After we will calculate the factors of 21294 and 21309 and find the biggest common factor number .

Step-1: Prime Factorization of 21294

Prime factors of 21294 are 2, 3, 7, 13. Prime factorization of 21294 in exponential form is:

21294 = 2¹ × 3² × 7¹ × 13²

Step-2: Prime Factorization of 21309

Prime factors of 21309 are 3, 7103. Prime factorization of 21309 in exponential form is:

21309 = 3¹ × 7103¹

Step-3: Factors of 21294

List of positive integer factors of 21294 that divides 21294 without a remainder.

1, 2, 3, 6, 7, 9, 13, 14, 18, 21, 26, 39, 42, 63, 78, 91, 117, 126, 169, 182, 234, 273, 338, 507, 546, 819, 1014, 1183, 1521, 1638, 2366, 3042, 3549, 7098, 10647

Step-4: Factors of 21309

List of positive integer factors of 21309 that divides 21294 without a remainder.

1, 3, 7103

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 21294 and 21309. The biggest common factor number is the GCF number.
So the greatest common factor 21294 and 21309 is 3.

Also check out the Least Common Multiple of 21294 and 21309