What is the Greatest Common Factor of 1800 and 1806?

Greatest common factor (GCF) of 1800 and 1806 is 6.

GCF(1800,1806) = 6

We will now calculate the prime factors of 1800 and 1806, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1800 and 1806.

How to find the GCF of 1800 and 1806?

We will first find the prime factorization of 1800 and 1806. After we will calculate the factors of 1800 and 1806 and find the biggest common factor number .

Step-1: Prime Factorization of 1800

Prime factors of 1800 are 2, 3, 5. Prime factorization of 1800 in exponential form is:

1800 = 2³ × 3² × 5²

Step-2: Prime Factorization of 1806

Prime factors of 1806 are 2, 3, 7, 43. Prime factorization of 1806 in exponential form is:

1806 = 2¹ × 3¹ × 7¹ × 43¹

Step-3: Factors of 1800

List of positive integer factors of 1800 that divides 1800 without a remainder.

1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 25, 30, 36, 40, 45, 50, 60, 72, 75, 90, 100, 120, 150, 180, 200, 225, 300, 360, 450, 600, 900

Step-4: Factors of 1806

List of positive integer factors of 1806 that divides 1800 without a remainder.

1, 2, 3, 6, 7, 14, 21, 42, 43, 86, 129, 258, 301, 602, 903

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1800 and 1806. The biggest common factor number is the GCF number.
So the greatest common factor 1800 and 1806 is 6.

Also check out the Least Common Multiple of 1800 and 1806