What is the Greatest Common Factor of 221 and 238?

Greatest common factor (GCF) of 221 and 238 is 17.

GCF(221,238) = 17

We will now calculate the prime factors of 221 and 238, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 221 and 238.

How to find the GCF of 221 and 238?

We will first find the prime factorization of 221 and 238. After we will calculate the factors of 221 and 238 and find the biggest common factor number .

Step-1: Prime Factorization of 221

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

221 = 13¹ × 17¹

Step-2: Prime Factorization of 238

Prime factors of 238 are 2, 7, 17. Prime factorization of 238 in exponential form is:

238 = 2¹ × 7¹ × 17¹

Step-3: Factors of 221

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

1, 13, 17

Step-4: Factors of 238

List of positive integer factors of 238 that divides 221 without a remainder.

1, 2, 7, 14, 17, 34, 119

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 221 and 238. The biggest common factor number is the GCF number.
So the greatest common factor 221 and 238 is 17.

Also check out the Least Common Multiple of 221 and 238