What is the Greatest Common Factor of 1209 and 1224?

Greatest common factor (GCF) of 1209 and 1224 is 3.

GCF(1209,1224) = 3

We will now calculate the prime factors of 1209 and 1224, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1209 and 1224.

How to find the GCF of 1209 and 1224?

We will first find the prime factorization of 1209 and 1224. After we will calculate the factors of 1209 and 1224 and find the biggest common factor number .

Step-1: Prime Factorization of 1209

Prime factors of 1209 are 3, 13, 31. Prime factorization of 1209 in exponential form is:

1209 = 3¹ × 13¹ × 31¹

Step-2: Prime Factorization of 1224

Prime factors of 1224 are 2, 3, 17. Prime factorization of 1224 in exponential form is:

1224 = 2³ × 3² × 17¹

Step-3: Factors of 1209

List of positive integer factors of 1209 that divides 1209 without a remainder.

1, 3, 13, 31, 39, 93, 403

Step-4: Factors of 1224

List of positive integer factors of 1224 that divides 1209 without a remainder.

1, 2, 3, 4, 6, 8, 9, 12, 17, 18, 24, 34, 36, 51, 68, 72, 102, 136, 153, 204, 306, 408, 612

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1209 and 1224. The biggest common factor number is the GCF number.
So the greatest common factor 1209 and 1224 is 3.

Also check out the Least Common Multiple of 1209 and 1224