What is the Greatest Common Factor of 238 and 252?

Greatest common factor (GCF) of 238 and 252 is 14.

GCF(238,252) = 14

We will now calculate the prime factors of 238 and 252, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 238 and 252.

How to find the GCF of 238 and 252?

We will first find the prime factorization of 238 and 252. After we will calculate the factors of 238 and 252 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 252

Prime factors of 252 are 2, 3, 7. Prime factorization of 252 in exponential form is:

252 = 2² × 3² × 7¹

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 252

List of positive integer factors of 252 that divides 238 without a remainder.

1, 2, 3, 4, 6, 7, 9, 12, 14, 18, 21, 28, 36, 42, 63, 84, 126

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 238 and 252. The biggest common factor number is the GCF number.
So the greatest common factor 238 and 252 is 14.

Also check out the Least Common Multiple of 238 and 252