What is the Greatest Common Factor of 1804 and 1822?

Greatest common factor (GCF) of 1804 and 1822 is 2.

GCF(1804,1822) = 2

We will now calculate the prime factors of 1804 and 1822, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1804 and 1822.

How to find the GCF of 1804 and 1822?

We will first find the prime factorization of 1804 and 1822. After we will calculate the factors of 1804 and 1822 and find the biggest common factor number .

Step-1: Prime Factorization of 1804

Prime factors of 1804 are 2, 11, 41. Prime factorization of 1804 in exponential form is:

1804 = 2² × 11¹ × 41¹

Step-2: Prime Factorization of 1822

Prime factors of 1822 are 2, 911. Prime factorization of 1822 in exponential form is:

1822 = 2¹ × 911¹

Step-3: Factors of 1804

List of positive integer factors of 1804 that divides 1804 without a remainder.

1, 2, 4, 11, 22, 41, 44, 82, 164, 451, 902

Step-4: Factors of 1822

List of positive integer factors of 1822 that divides 1804 without a remainder.

1, 2, 911

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1804 and 1822. The biggest common factor number is the GCF number.
So the greatest common factor 1804 and 1822 is 2.

Also check out the Least Common Multiple of 1804 and 1822