What is the Greatest Common Factor of 51000 and 51004?

Greatest common factor (GCF) of 51000 and 51004 is 4.

GCF(51000,51004) = 4

We will now calculate the prime factors of 51000 and 51004, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 51000 and 51004.

How to find the GCF of 51000 and 51004?

We will first find the prime factorization of 51000 and 51004. After we will calculate the factors of 51000 and 51004 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 51004

Prime factors of 51004 are 2, 41, 311. Prime factorization of 51004 in exponential form is:

51004 = 2² × 41¹ × 311¹

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 51004

List of positive integer factors of 51004 that divides 51000 without a remainder.

1, 2, 4, 41, 82, 164, 311, 622, 1244, 12751, 25502

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 51000 and 51004. The biggest common factor number is the GCF number.
So the greatest common factor 51000 and 51004 is 4.

Also check out the Least Common Multiple of 51000 and 51004