What is the Greatest Common Factor of 5120 and 5130?

Greatest common factor (GCF) of 5120 and 5130 is 10.

GCF(5120,5130) = 10

We will now calculate the prime factors of 5120 and 5130, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 5120 and 5130.

How to find the GCF of 5120 and 5130?

We will first find the prime factorization of 5120 and 5130. After we will calculate the factors of 5120 and 5130 and find the biggest common factor number .

Step-1: Prime Factorization of 5120

Prime factors of 5120 are 2, 5. Prime factorization of 5120 in exponential form is:

5120 = 2¹⁰ × 5¹

Step-2: 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-3: Factors of 5120

List of positive integer factors of 5120 that divides 5120 without a remainder.

1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 64, 80, 128, 160, 256, 320, 512, 640, 1024, 1280, 2560

Step-4: Factors of 5130

List of positive integer factors of 5130 that divides 5120 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 5120 and 5130. The biggest common factor number is the GCF number.
So the greatest common factor 5120 and 5130 is 10.

Also check out the Least Common Multiple of 5120 and 5130