What is the Greatest Common Factor of 19314 and 19322?

Greatest common factor (GCF) of 19314 and 19322 is 2.

GCF(19314,19322) = 2

We will now calculate the prime factors of 19314 and 19322, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 19314 and 19322.

How to find the GCF of 19314 and 19322?

We will first find the prime factorization of 19314 and 19322. After we will calculate the factors of 19314 and 19322 and find the biggest common factor number .

Step-1: Prime Factorization of 19314

Prime factors of 19314 are 2, 3, 29, 37. Prime factorization of 19314 in exponential form is:

19314 = 2¹ × 3² × 29¹ × 37¹

Step-2: Prime Factorization of 19322

Prime factors of 19322 are 2, 9661. Prime factorization of 19322 in exponential form is:

19322 = 2¹ × 9661¹

Step-3: Factors of 19314

List of positive integer factors of 19314 that divides 19314 without a remainder.

1, 2, 3, 6, 9, 18, 29, 37, 58, 74, 87, 111, 174, 222, 261, 333, 522, 666, 1073, 2146, 3219, 6438, 9657

Step-4: Factors of 19322

List of positive integer factors of 19322 that divides 19314 without a remainder.

1, 2, 9661

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 19314 and 19322. The biggest common factor number is the GCF number.
So the greatest common factor 19314 and 19322 is 2.

Also check out the Least Common Multiple of 19314 and 19322