What is the Greatest Common Factor of 11209 and 11214?

Greatest common factor (GCF) of 11209 and 11214 is 1.

GCF(11209,11214) = 1

We will now calculate the prime factors of 11209 and 11214, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 11209 and 11214.

How to find the GCF of 11209 and 11214?

We will first find the prime factorization of 11209 and 11214. After we will calculate the factors of 11209 and 11214 and find the biggest common factor number .

Step-1: Prime Factorization of 11209

Prime factors of 11209 are 11, 1019. Prime factorization of 11209 in exponential form is:

11209 = 11¹ × 1019¹

Step-2: Prime Factorization of 11214

Prime factors of 11214 are 2, 3, 7, 89. Prime factorization of 11214 in exponential form is:

11214 = 2¹ × 3² × 7¹ × 89¹

Step-3: Factors of 11209

List of positive integer factors of 11209 that divides 11209 without a remainder.

1, 11, 1019

Step-4: Factors of 11214

List of positive integer factors of 11214 that divides 11209 without a remainder.

1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 63, 89, 126, 178, 267, 534, 623, 801, 1246, 1602, 1869, 3738, 5607

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 11209 and 11214. The biggest common factor number is the GCF number.
So the greatest common factor 11209 and 11214 is 1.

Also check out the Least Common Multiple of 11209 and 11214