What is the Greatest Common Factor of 1809 and 1829?

Greatest common factor (GCF) of 1809 and 1829 is 1.

GCF(1809,1829) = 1

We will now calculate the prime factors of 1809 and 1829, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1809 and 1829.

How to find the GCF of 1809 and 1829?

We will first find the prime factorization of 1809 and 1829. After we will calculate the factors of 1809 and 1829 and find the biggest common factor number .

Step-1: Prime Factorization of 1809

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

1809 = 3³ × 67¹

Step-2: Prime Factorization of 1829

Prime factors of 1829 are 31, 59. Prime factorization of 1829 in exponential form is:

1829 = 31¹ × 59¹

Step-3: Factors of 1809

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

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

Step-4: Factors of 1829

List of positive integer factors of 1829 that divides 1809 without a remainder.

1, 31, 59

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1809 and 1829. The biggest common factor number is the GCF number.
So the greatest common factor 1809 and 1829 is 1.

Also check out the Least Common Multiple of 1809 and 1829