What is the Greatest Common Factor of 224 and 238?

Greatest common factor (GCF) of 224 and 238 is 14.

GCF(224,238) = 14

We will now calculate the prime factors of 224 and 238, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 224 and 238.

How to find the GCF of 224 and 238?

We will first find the prime factorization of 224 and 238. After we will calculate the factors of 224 and 238 and find the biggest common factor number .

Step-1: Prime Factorization of 224

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

224 = 2⁵ × 7¹

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 224

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

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

Step-4: Factors of 238

List of positive integer factors of 238 that divides 224 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 224 and 238. The biggest common factor number is the GCF number.
So the greatest common factor 224 and 238 is 14.

Also check out the Least Common Multiple of 224 and 238