What is the Greatest Common Factor of 27209 and 27222?

Greatest common factor (GCF) of 27209 and 27222 is 13.

GCF(27209,27222) = 13

We will now calculate the prime factors of 27209 and 27222, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 27209 and 27222.

How to find the GCF of 27209 and 27222?

We will first find the prime factorization of 27209 and 27222. After we will calculate the factors of 27209 and 27222 and find the biggest common factor number .

Step-1: Prime Factorization of 27209

Prime factors of 27209 are 7, 13, 23. Prime factorization of 27209 in exponential form is:

27209 = 7¹ × 13² × 23¹

Step-2: Prime Factorization of 27222

Prime factors of 27222 are 2, 3, 13, 349. Prime factorization of 27222 in exponential form is:

27222 = 2¹ × 3¹ × 13¹ × 349¹

Step-3: Factors of 27209

List of positive integer factors of 27209 that divides 27209 without a remainder.

1, 7, 13, 23, 91, 161, 169, 299, 1183, 2093, 3887

Step-4: Factors of 27222

List of positive integer factors of 27222 that divides 27209 without a remainder.

1, 2, 3, 6, 13, 26, 39, 78, 349, 698, 1047, 2094, 4537, 9074, 13611

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 27209 and 27222. The biggest common factor number is the GCF number.
So the greatest common factor 27209 and 27222 is 13.

Also check out the Least Common Multiple of 27209 and 27222