What is the Greatest Common Factor of 19209 and 19228?

Greatest common factor (GCF) of 19209 and 19228 is 19.

GCF(19209,19228) = 19

We will now calculate the prime factors of 19209 and 19228, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 19209 and 19228.

How to find the GCF of 19209 and 19228?

We will first find the prime factorization of 19209 and 19228. After we will calculate the factors of 19209 and 19228 and find the biggest common factor number .

Step-1: Prime Factorization of 19209

Prime factors of 19209 are 3, 19, 337. Prime factorization of 19209 in exponential form is:

19209 = 3¹ × 19¹ × 337¹

Step-2: Prime Factorization of 19228

Prime factors of 19228 are 2, 11, 19, 23. Prime factorization of 19228 in exponential form is:

19228 = 2² × 11¹ × 19¹ × 23¹

Step-3: Factors of 19209

List of positive integer factors of 19209 that divides 19209 without a remainder.

1, 3, 19, 57, 337, 1011, 6403

Step-4: Factors of 19228

List of positive integer factors of 19228 that divides 19209 without a remainder.

1, 2, 4, 11, 19, 22, 23, 38, 44, 46, 76, 92, 209, 253, 418, 437, 506, 836, 874, 1012, 1748, 4807, 9614

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 19209 and 19228. The biggest common factor number is the GCF number.
So the greatest common factor 19209 and 19228 is 19.

Also check out the Least Common Multiple of 19209 and 19228