What is the Greatest Common Factor of 5238 and 5258?

Greatest common factor (GCF) of 5238 and 5258 is 2.

GCF(5238,5258) = 2

We will now calculate the prime factors of 5238 and 5258, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 5238 and 5258.

How to find the GCF of 5238 and 5258?

We will first find the prime factorization of 5238 and 5258. After we will calculate the factors of 5238 and 5258 and find the biggest common factor number .

Step-1: Prime Factorization of 5238

Prime factors of 5238 are 2, 3, 97. Prime factorization of 5238 in exponential form is:

5238 = 2¹ × 3³ × 97¹

Step-2: Prime Factorization of 5258

Prime factors of 5258 are 2, 11, 239. Prime factorization of 5258 in exponential form is:

5258 = 2¹ × 11¹ × 239¹

Step-3: Factors of 5238

List of positive integer factors of 5238 that divides 5238 without a remainder.

1, 2, 3, 6, 9, 18, 27, 54, 97, 194, 291, 582, 873, 1746, 2619

Step-4: Factors of 5258

List of positive integer factors of 5258 that divides 5238 without a remainder.

1, 2, 11, 22, 239, 478, 2629

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 5238 and 5258. The biggest common factor number is the GCF number.
So the greatest common factor 5238 and 5258 is 2.

Also check out the Least Common Multiple of 5238 and 5258