What is the Greatest Common Factor of 51000 and 51006?

Greatest common factor (GCF) of 51000 and 51006 is 6.

GCF(51000,51006) = 6

We will now calculate the prime factors of 51000 and 51006, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 51000 and 51006.

How to find the GCF of 51000 and 51006?

We will first find the prime factorization of 51000 and 51006. After we will calculate the factors of 51000 and 51006 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 51006

Prime factors of 51006 are 2, 3, 8501. Prime factorization of 51006 in exponential form is:

51006 = 2¹ × 3¹ × 8501¹

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 51006

List of positive integer factors of 51006 that divides 51000 without a remainder.

1, 2, 3, 6, 8501, 17002, 25503

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 51000 and 51006. The biggest common factor number is the GCF number.
So the greatest common factor 51000 and 51006 is 6.

Also check out the Least Common Multiple of 51000 and 51006