What is the Greatest Common Factor of 1800 and 1810?

Greatest common factor (GCF) of 1800 and 1810 is 10.

GCF(1800,1810) = 10

We will now calculate the prime factors of 1800 and 1810, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1800 and 1810.

How to find the GCF of 1800 and 1810?

We will first find the prime factorization of 1800 and 1810. After we will calculate the factors of 1800 and 1810 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 1810

Prime factors of 1810 are 2, 5, 181. Prime factorization of 1810 in exponential form is:

1810 = 2¹ × 5¹ × 181¹

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 1810

List of positive integer factors of 1810 that divides 1800 without a remainder.

1, 2, 5, 10, 181, 362, 905

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1800 and 1810. The biggest common factor number is the GCF number.
So the greatest common factor 1800 and 1810 is 10.

Also check out the Least Common Multiple of 1800 and 1810