What is the Greatest Common Factor of 51000 and 51007?

Greatest common factor (GCF) of 51000 and 51007 is 1.

GCF(51000,51007) = 1

We will now calculate the prime factors of 51000 and 51007, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 51000 and 51007.

How to find the GCF of 51000 and 51007?

We will first find the prime factorization of 51000 and 51007. After we will calculate the factors of 51000 and 51007 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 51007

Prime factors of 51007 are 11, 4637. Prime factorization of 51007 in exponential form is:

51007 = 11¹ × 4637¹

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 51007

List of positive integer factors of 51007 that divides 51000 without a remainder.

1, 11, 4637

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 51000 and 51007. The biggest common factor number is the GCF number.
So the greatest common factor 51000 and 51007 is 1.

Also check out the Least Common Multiple of 51000 and 51007