What is the Greatest Common Factor of 5100 and 5120?

Greatest common factor (GCF) of 5100 and 5120 is 20.

GCF(5100,5120) = 20

We will now calculate the prime factors of 5100 and 5120, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 5100 and 5120.

How to find the GCF of 5100 and 5120?

We will first find the prime factorization of 5100 and 5120. After we will calculate the factors of 5100 and 5120 and find the biggest common factor number .

Step-1: Prime Factorization of 5100

Prime factors of 5100 are 2, 3, 5, 17. Prime factorization of 5100 in exponential form is:

5100 = 2² × 3¹ × 5² × 17¹

Step-2: Prime Factorization of 5120

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

5120 = 2¹⁰ × 5¹

Step-3: Factors of 5100

List of positive integer factors of 5100 that divides 5100 without a remainder.

1, 2, 3, 4, 5, 6, 10, 12, 15, 17, 20, 25, 30, 34, 50, 51, 60, 68, 75, 85, 100, 102, 150, 170, 204, 255, 300, 340, 425, 510, 850, 1020, 1275, 1700, 2550

Step-4: Factors of 5120

List of positive integer factors of 5120 that divides 5100 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 5100 and 5120. The biggest common factor number is the GCF number.
So the greatest common factor 5100 and 5120 is 20.

Also check out the Least Common Multiple of 5100 and 5120