What is the Greatest Common Factor of 5138 and 5152?

Greatest common factor (GCF) of 5138 and 5152 is 14.

GCF(5138,5152) = 14

We will now calculate the prime factors of 5138 and 5152, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 5138 and 5152.

How to find the GCF of 5138 and 5152?

We will first find the prime factorization of 5138 and 5152. After we will calculate the factors of 5138 and 5152 and find the biggest common factor number .

Step-1: Prime Factorization of 5138

Prime factors of 5138 are 2, 7, 367. Prime factorization of 5138 in exponential form is:

5138 = 2¹ × 7¹ × 367¹

Step-2: Prime Factorization of 5152

Prime factors of 5152 are 2, 7, 23. Prime factorization of 5152 in exponential form is:

5152 = 2⁵ × 7¹ × 23¹

Step-3: Factors of 5138

List of positive integer factors of 5138 that divides 5138 without a remainder.

1, 2, 7, 14, 367, 734, 2569

Step-4: Factors of 5152

List of positive integer factors of 5152 that divides 5138 without a remainder.

1, 2, 4, 7, 8, 14, 16, 23, 28, 32, 46, 56, 92, 112, 161, 184, 224, 322, 368, 644, 736, 1288, 2576

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 5138 and 5152. The biggest common factor number is the GCF number.
So the greatest common factor 5138 and 5152 is 14.

Also check out the Least Common Multiple of 5138 and 5152