What is the Greatest Common Factor of 2209 and 2224?

Greatest common factor (GCF) of 2209 and 2224 is 1.

GCF(2209,2224) = 1

We will now calculate the prime factors of 2209 and 2224, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 2209 and 2224.

How to find the GCF of 2209 and 2224?

We will first find the prime factorization of 2209 and 2224. After we will calculate the factors of 2209 and 2224 and find the biggest common factor number .

Step-1: Prime Factorization of 2209

Prime factors of 2209 are 47. Prime factorization of 2209 in exponential form is:

2209 = 47²

Step-2: Prime Factorization of 2224

Prime factors of 2224 are 2, 139. Prime factorization of 2224 in exponential form is:

2224 = 2⁴ × 139¹

Step-3: Factors of 2209

List of positive integer factors of 2209 that divides 2209 without a remainder.

1, 47

Step-4: Factors of 2224

List of positive integer factors of 2224 that divides 2209 without a remainder.

1, 2, 4, 8, 16, 139, 278, 556, 1112

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 2209 and 2224. The biggest common factor number is the GCF number.
So the greatest common factor 2209 and 2224 is 1.

Also check out the Least Common Multiple of 2209 and 2224