What is the Greatest Common Factor of 1800 and 1808?

Greatest common factor (GCF) of 1800 and 1808 is 8.

GCF(1800,1808) = 8

We will now calculate the prime factors of 1800 and 1808, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1800 and 1808.

How to find the GCF of 1800 and 1808?

We will first find the prime factorization of 1800 and 1808. After we will calculate the factors of 1800 and 1808 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 1808

Prime factors of 1808 are 2, 113. Prime factorization of 1808 in exponential form is:

1808 = 2⁴ × 113¹

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 1808

List of positive integer factors of 1808 that divides 1800 without a remainder.

1, 2, 4, 8, 16, 113, 226, 452, 904

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1800 and 1808. The biggest common factor number is the GCF number.
So the greatest common factor 1800 and 1808 is 8.

Also check out the Least Common Multiple of 1800 and 1808