What is the Greatest Common Factor of 5124 and 5138?

Greatest common factor (GCF) of 5124 and 5138 is 14.

GCF(5124,5138) = 14

We will now calculate the prime factors of 5124 and 5138, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 5124 and 5138.

How to find the GCF of 5124 and 5138?

We will first find the prime factorization of 5124 and 5138. After we will calculate the factors of 5124 and 5138 and find the biggest common factor number .

Step-1: Prime Factorization of 5124

Prime factors of 5124 are 2, 3, 7, 61. Prime factorization of 5124 in exponential form is:

5124 = 2² × 3¹ × 7¹ × 61¹

Step-2: 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-3: Factors of 5124

List of positive integer factors of 5124 that divides 5124 without a remainder.

1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 61, 84, 122, 183, 244, 366, 427, 732, 854, 1281, 1708, 2562

Step-4: Factors of 5138

List of positive integer factors of 5138 that divides 5124 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 5124 and 5138. The biggest common factor number is the GCF number.
So the greatest common factor 5124 and 5138 is 14.

Also check out the Least Common Multiple of 5124 and 5138