What is the Greatest Common Factor of 205 and 224?

Greatest common factor (GCF) of 205 and 224 is 1.

GCF(205,224) = 1

We will now calculate the prime factors of 205 and 224, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 205 and 224.

How to find the GCF of 205 and 224?

We will first find the prime factorization of 205 and 224. After we will calculate the factors of 205 and 224 and find the biggest common factor number .

Step-1: Prime Factorization of 205

Prime factors of 205 are 5, 41. Prime factorization of 205 in exponential form is:

205 = 5¹ × 41¹

Step-2: Prime Factorization of 224

Prime factors of 224 are 2, 7. Prime factorization of 224 in exponential form is:

224 = 2⁵ × 7¹

Step-3: Factors of 205

List of positive integer factors of 205 that divides 205 without a remainder.

1, 5, 41

Step-4: Factors of 224

List of positive integer factors of 224 that divides 205 without a remainder.

1, 2, 4, 7, 8, 14, 16, 28, 32, 56, 112

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 205 and 224. The biggest common factor number is the GCF number.
So the greatest common factor 205 and 224 is 1.

Also check out the Least Common Multiple of 205 and 224