What is the Greatest Common Factor of 1809 and 1815?

Greatest common factor (GCF) of 1809 and 1815 is 3.

GCF(1809,1815) = 3

We will now calculate the prime factors of 1809 and 1815, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1809 and 1815.

How to find the GCF of 1809 and 1815?

We will first find the prime factorization of 1809 and 1815. After we will calculate the factors of 1809 and 1815 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 1815

Prime factors of 1815 are 3, 5, 11. Prime factorization of 1815 in exponential form is:

1815 = 3¹ × 5¹ × 11²

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 1815

List of positive integer factors of 1815 that divides 1809 without a remainder.

1, 3, 5, 11, 15, 33, 55, 121, 165, 363, 605

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1809 and 1815. The biggest common factor number is the GCF number.
So the greatest common factor 1809 and 1815 is 3.

Also check out the Least Common Multiple of 1809 and 1815