What is the Greatest Common Factor of 19209 and 19224?

Greatest common factor (GCF) of 19209 and 19224 is 3.

GCF(19209,19224) = 3

We will now calculate the prime factors of 19209 and 19224, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 19209 and 19224.

How to find the GCF of 19209 and 19224?

We will first find the prime factorization of 19209 and 19224. After we will calculate the factors of 19209 and 19224 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 19224

Prime factors of 19224 are 2, 3, 89. Prime factorization of 19224 in exponential form is:

19224 = 2³ × 3³ × 89¹

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 19224

List of positive integer factors of 19224 that divides 19209 without a remainder.

1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 89, 108, 178, 216, 267, 356, 534, 712, 801, 1068, 1602, 2136, 2403, 3204, 4806, 6408, 9612

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 19209 and 19224. The biggest common factor number is the GCF number.
So the greatest common factor 19209 and 19224 is 3.

Also check out the Least Common Multiple of 19209 and 19224