What is the Greatest Common Factor of 238 and 258?

Greatest common factor (GCF) of 238 and 258 is 2.

GCF(238,258) = 2

We will now calculate the prime factors of 238 and 258, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 238 and 258.

How to find the GCF of 238 and 258?

We will first find the prime factorization of 238 and 258. After we will calculate the factors of 238 and 258 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 258

Prime factors of 258 are 2, 3, 43. Prime factorization of 258 in exponential form is:

258 = 2¹ × 3¹ × 43¹

Step-3: Factors of 238

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

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

Step-4: Factors of 258

List of positive integer factors of 258 that divides 238 without a remainder.

1, 2, 3, 6, 43, 86, 129

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 238 and 258. The biggest common factor number is the GCF number.
So the greatest common factor 238 and 258 is 2.

Also check out the Least Common Multiple of 238 and 258