What is the Greatest Common Factor of 51000 and 51017?

Greatest common factor (GCF) of 51000 and 51017 is 17.

GCF(51000,51017) = 17

We will now calculate the prime factors of 51000 and 51017, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 51000 and 51017.

How to find the GCF of 51000 and 51017?

We will first find the prime factorization of 51000 and 51017. After we will calculate the factors of 51000 and 51017 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 51017

Prime factors of 51017 are 17, 3001. Prime factorization of 51017 in exponential form is:

51017 = 17¹ × 3001¹

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 51017

List of positive integer factors of 51017 that divides 51000 without a remainder.

1, 17, 3001

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 51000 and 51017. The biggest common factor number is the GCF number.
So the greatest common factor 51000 and 51017 is 17.

Also check out the Least Common Multiple of 51000 and 51017