What is the Greatest Common Factor of 238 and 254?

Greatest common factor (GCF) of 238 and 254 is 2.

GCF(238,254) = 2

We will now calculate the prime factors of 238 and 254, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 238 and 254.

How to find the GCF of 238 and 254?

We will first find the prime factorization of 238 and 254. After we will calculate the factors of 238 and 254 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 254

Prime factors of 254 are 2, 127. Prime factorization of 254 in exponential form is:

254 = 2¹ × 127¹

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 254

List of positive integer factors of 254 that divides 238 without a remainder.

1, 2, 127

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 238 and 254. The biggest common factor number is the GCF number.
So the greatest common factor 238 and 254 is 2.

Also check out the Least Common Multiple of 238 and 254