What is the Greatest Common Factor of 7238 and 7252?

Greatest common factor (GCF) of 7238 and 7252 is 14.

GCF(7238,7252) = 14

We will now calculate the prime factors of 7238 and 7252, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 7238 and 7252.

How to find the GCF of 7238 and 7252?

We will first find the prime factorization of 7238 and 7252. After we will calculate the factors of 7238 and 7252 and find the biggest common factor number .

Step-1: Prime Factorization of 7238

Prime factors of 7238 are 2, 7, 11, 47. Prime factorization of 7238 in exponential form is:

7238 = 2¹ × 7¹ × 11¹ × 47¹

Step-2: Prime Factorization of 7252

Prime factors of 7252 are 2, 7, 37. Prime factorization of 7252 in exponential form is:

7252 = 2² × 7² × 37¹

Step-3: Factors of 7238

List of positive integer factors of 7238 that divides 7238 without a remainder.

1, 2, 7, 11, 14, 22, 47, 77, 94, 154, 329, 517, 658, 1034, 3619

Step-4: Factors of 7252

List of positive integer factors of 7252 that divides 7238 without a remainder.

1, 2, 4, 7, 14, 28, 37, 49, 74, 98, 148, 196, 259, 518, 1036, 1813, 3626

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 7238 and 7252. The biggest common factor number is the GCF number.
So the greatest common factor 7238 and 7252 is 14.

Also check out the Least Common Multiple of 7238 and 7252