What is the Greatest Common Factor of 2205 and 2224?

Greatest common factor (GCF) of 2205 and 2224 is 1.

GCF(2205,2224) = 1

We will now calculate the prime factors of 2205 and 2224, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 2205 and 2224.

How to find the GCF of 2205 and 2224?

We will first find the prime factorization of 2205 and 2224. After we will calculate the factors of 2205 and 2224 and find the biggest common factor number .

Step-1: Prime Factorization of 2205

Prime factors of 2205 are 3, 5, 7. Prime factorization of 2205 in exponential form is:

2205 = 3² × 5¹ × 7²

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 2205

List of positive integer factors of 2205 that divides 2205 without a remainder.

1, 3, 5, 7, 9, 15, 21, 35, 45, 49, 63, 105, 147, 245, 315, 441, 735

Step-4: Factors of 2224

List of positive integer factors of 2224 that divides 2205 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 2205 and 2224. The biggest common factor number is the GCF number.
So the greatest common factor 2205 and 2224 is 1.

Also check out the Least Common Multiple of 2205 and 2224