What is the Greatest Common Factor of 1800 and 1805?

Greatest common factor (GCF) of 1800 and 1805 is 5.

GCF(1800,1805) = 5

We will now calculate the prime factors of 1800 and 1805, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1800 and 1805.

How to find the GCF of 1800 and 1805?

We will first find the prime factorization of 1800 and 1805. After we will calculate the factors of 1800 and 1805 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 1805

Prime factors of 1805 are 5, 19. Prime factorization of 1805 in exponential form is:

1805 = 5¹ × 19²

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 1805

List of positive integer factors of 1805 that divides 1800 without a remainder.

1, 5, 19, 95, 361

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1800 and 1805. The biggest common factor number is the GCF number.
So the greatest common factor 1800 and 1805 is 5.

Also check out the Least Common Multiple of 1800 and 1805