What is the Greatest Common Factor of 1800 and 1814?

Greatest common factor (GCF) of 1800 and 1814 is 2.

GCF(1800,1814) = 2

We will now calculate the prime factors of 1800 and 1814, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1800 and 1814.

How to find the GCF of 1800 and 1814?

We will first find the prime factorization of 1800 and 1814. After we will calculate the factors of 1800 and 1814 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 1814

Prime factors of 1814 are 2, 907. Prime factorization of 1814 in exponential form is:

1814 = 2¹ × 907¹

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 1814

List of positive integer factors of 1814 that divides 1800 without a remainder.

1, 2, 907

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1800 and 1814. The biggest common factor number is the GCF number.
So the greatest common factor 1800 and 1814 is 2.

Also check out the Least Common Multiple of 1800 and 1814