What is the Greatest Common Factor of 1791 and 1809?

Greatest common factor (GCF) of 1791 and 1809 is 9.

GCF(1791,1809) = 9

We will now calculate the prime factors of 1791 and 1809, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1791 and 1809.

How to find the GCF of 1791 and 1809?

We will first find the prime factorization of 1791 and 1809. After we will calculate the factors of 1791 and 1809 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 1809

Prime factors of 1809 are 3, 67. Prime factorization of 1809 in exponential form is:

1809 = 3³ × 67¹

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 1809

List of positive integer factors of 1809 that divides 1791 without a remainder.

1, 3, 9, 27, 67, 201, 603

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1791 and 1809. The biggest common factor number is the GCF number.
So the greatest common factor 1791 and 1809 is 9.

Also check out the Least Common Multiple of 1791 and 1809