What is the Greatest Common Factor of 51000 and 51019?

Greatest common factor (GCF) of 51000 and 51019 is 1.

GCF(51000,51019) = 1

We will now calculate the prime factors of 51000 and 51019, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 51000 and 51019.

How to find the GCF of 51000 and 51019?

We will first find the prime factorization of 51000 and 51019. After we will calculate the factors of 51000 and 51019 and find the biggest common factor number .

Step-1: Prime Factorization of 51000

Prime factors of 51000 are 2, 3, 5, 17. Prime factorization of 51000 in exponential form is:

51000 = 2³ × 3¹ × 5³ × 17¹

Step-2: Prime Factorization of 51019

Prime factors of 51019 are 163, 313. Prime factorization of 51019 in exponential form is:

51019 = 163¹ × 313¹

Step-3: Factors of 51000

List of positive integer factors of 51000 that divides 51000 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 17, 20, 24, 25, 30, 34, 40, 50, 51, 60, 68, 75, 85, 100, 102, 120, 125, 136, 150, 170, 200, 204, 250, 255, 300, 340, 375, 408, 425, 500, 510, 600, 680, 750, 850, 1000, 1020, 1275, 1500, 1700, 2040, 2125, 2550, 3000, 3400, 4250, 5100, 6375, 8500, 10200, 12750, 17000, 25500

Step-4: Factors of 51019

List of positive integer factors of 51019 that divides 51000 without a remainder.

1, 163, 313

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 51000 and 51019. The biggest common factor number is the GCF number.
So the greatest common factor 51000 and 51019 is 1.

Also check out the Least Common Multiple of 51000 and 51019