What is the Greatest Common Factor of 19299 and 19314?

Greatest common factor (GCF) of 19299 and 19314 is 3.

GCF(19299,19314) = 3

We will now calculate the prime factors of 19299 and 19314, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 19299 and 19314.

How to find the GCF of 19299 and 19314?

We will first find the prime factorization of 19299 and 19314. After we will calculate the factors of 19299 and 19314 and find the biggest common factor number .

Step-1: Prime Factorization of 19299

Prime factors of 19299 are 3, 7, 919. Prime factorization of 19299 in exponential form is:

19299 = 3¹ × 7¹ × 919¹

Step-2: 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-3: Factors of 19299

List of positive integer factors of 19299 that divides 19299 without a remainder.

1, 3, 7, 21, 919, 2757, 6433

Step-4: Factors of 19314

List of positive integer factors of 19314 that divides 19299 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 19299 and 19314. The biggest common factor number is the GCF number.
So the greatest common factor 19299 and 19314 is 3.

Also check out the Least Common Multiple of 19299 and 19314