What is the Greatest Common Factor of 1791 and 1800?

Greatest common factor (GCF) of 1791 and 1800 is 9.

GCF(1791,1800) = 9

We will now calculate the prime factors of 1791 and 1800, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1791 and 1800.

How to find the GCF of 1791 and 1800?

We will first find the prime factorization of 1791 and 1800. After we will calculate the factors of 1791 and 1800 and find the biggest common factor number .

Step-1: Prime Factorization of 1791

Prime factors of 1791 are 3, 199. Prime factorization of 1791 in exponential form is:

1791 = 3² × 199¹

Step-2: 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-3: Factors of 1791

List of positive integer factors of 1791 that divides 1791 without a remainder.

1, 3, 9, 199, 597

Step-4: Factors of 1800

List of positive integer factors of 1800 that divides 1791 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1791 and 1800. The biggest common factor number is the GCF number.
So the greatest common factor 1791 and 1800 is 9.

Also check out the Least Common Multiple of 1791 and 1800