What is the Greatest Common Factor of 1809 and 1824?

Greatest common factor (GCF) of 1809 and 1824 is 3.

GCF(1809,1824) = 3

We will now calculate the prime factors of 1809 and 1824, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1809 and 1824.

How to find the GCF of 1809 and 1824?

We will first find the prime factorization of 1809 and 1824. After we will calculate the factors of 1809 and 1824 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 1824

Prime factors of 1824 are 2, 3, 19. Prime factorization of 1824 in exponential form is:

1824 = 2⁵ × 3¹ × 19¹

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 1824

List of positive integer factors of 1824 that divides 1809 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 19, 24, 32, 38, 48, 57, 76, 96, 114, 152, 228, 304, 456, 608, 912

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1809 and 1824. The biggest common factor number is the GCF number.
So the greatest common factor 1809 and 1824 is 3.

Also check out the Least Common Multiple of 1809 and 1824