What is the Greatest Common Factor of 36805 and 36822?

Greatest common factor (GCF) of 36805 and 36822 is 17.

GCF(36805,36822) = 17

We will now calculate the prime factors of 36805 and 36822, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 36805 and 36822.

How to find the GCF of 36805 and 36822?

We will first find the prime factorization of 36805 and 36822. After we will calculate the factors of 36805 and 36822 and find the biggest common factor number .

Step-1: Prime Factorization of 36805

Prime factors of 36805 are 5, 17, 433. Prime factorization of 36805 in exponential form is:

36805 = 5¹ × 17¹ × 433¹

Step-2: Prime Factorization of 36822

Prime factors of 36822 are 2, 3, 17, 19. Prime factorization of 36822 in exponential form is:

36822 = 2¹ × 3¹ × 17¹ × 19²

Step-3: Factors of 36805

List of positive integer factors of 36805 that divides 36805 without a remainder.

1, 5, 17, 85, 433, 2165, 7361

Step-4: Factors of 36822

List of positive integer factors of 36822 that divides 36805 without a remainder.

1, 2, 3, 6, 17, 19, 34, 38, 51, 57, 102, 114, 323, 361, 646, 722, 969, 1083, 1938, 2166, 6137, 12274, 18411

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 36805 and 36822. The biggest common factor number is the GCF number.
So the greatest common factor 36805 and 36822 is 17.

Also check out the Least Common Multiple of 36805 and 36822