What is the Greatest Common Factor of 1805 and 1824?

Greatest common factor (GCF) of 1805 and 1824 is 19.

GCF(1805,1824) = 19

We will now calculate the prime factors of 1805 and 1824, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1805 and 1824.

How to find the GCF of 1805 and 1824?

We will first find the prime factorization of 1805 and 1824. After we will calculate the factors of 1805 and 1824 and find the biggest common factor number .

Step-1: Prime Factorization of 1805

Prime factors of 1805 are 5, 19. Prime factorization of 1805 in exponential form is:

1805 = 5¹ × 19²

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 1805

List of positive integer factors of 1805 that divides 1805 without a remainder.

1, 5, 19, 95, 361

Step-4: Factors of 1824

List of positive integer factors of 1824 that divides 1805 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 1805 and 1824. The biggest common factor number is the GCF number.
So the greatest common factor 1805 and 1824 is 19.

Also check out the Least Common Multiple of 1805 and 1824