What is the Greatest Common Factor of 205 and 221?

Greatest common factor (GCF) of 205 and 221 is 1.

GCF(205,221) = 1

We will now calculate the prime factors of 205 and 221, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 205 and 221.

How to find the GCF of 205 and 221?

We will first find the prime factorization of 205 and 221. After we will calculate the factors of 205 and 221 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 221

Prime factors of 221 are 13, 17. Prime factorization of 221 in exponential form is:

221 = 13¹ × 17¹

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 221

List of positive integer factors of 221 that divides 205 without a remainder.

1, 13, 17

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 205 and 221. The biggest common factor number is the GCF number.
So the greatest common factor 205 and 221 is 1.

Also check out the Least Common Multiple of 205 and 221