What is the Greatest Common Factor of 5130 and 5138?

Greatest common factor (GCF) of 5130 and 5138 is 2.

GCF(5130,5138) = 2

We will now calculate the prime factors of 5130 and 5138, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 5130 and 5138.

How to find the GCF of 5130 and 5138?

We will first find the prime factorization of 5130 and 5138. After we will calculate the factors of 5130 and 5138 and find the biggest common factor number .

Step-1: Prime Factorization of 5130

Prime factors of 5130 are 2, 3, 5, 19. Prime factorization of 5130 in exponential form is:

5130 = 2¹ × 3³ × 5¹ × 19¹

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 5130

List of positive integer factors of 5130 that divides 5130 without a remainder.

1, 2, 3, 5, 6, 9, 10, 15, 18, 19, 27, 30, 38, 45, 54, 57, 90, 95, 114, 135, 171, 190, 270, 285, 342, 513, 570, 855, 1026, 1710, 2565

Step-4: Factors of 5138

List of positive integer factors of 5138 that divides 5130 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 5130 and 5138. The biggest common factor number is the GCF number.
So the greatest common factor 5130 and 5138 is 2.

Also check out the Least Common Multiple of 5130 and 5138