What is the Greatest Common Factor of 7209 and 7224?

Greatest common factor (GCF) of 7209 and 7224 is 3.

GCF(7209,7224) = 3

We will now calculate the prime factors of 7209 and 7224, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 7209 and 7224.

How to find the GCF of 7209 and 7224?

We will first find the prime factorization of 7209 and 7224. After we will calculate the factors of 7209 and 7224 and find the biggest common factor number .

Step-1: Prime Factorization of 7209

Prime factors of 7209 are 3, 89. Prime factorization of 7209 in exponential form is:

7209 = 3⁴ × 89¹

Step-2: Prime Factorization of 7224

Prime factors of 7224 are 2, 3, 7, 43. Prime factorization of 7224 in exponential form is:

7224 = 2³ × 3¹ × 7¹ × 43¹

Step-3: Factors of 7209

List of positive integer factors of 7209 that divides 7209 without a remainder.

1, 3, 9, 27, 81, 89, 267, 801, 2403

Step-4: Factors of 7224

List of positive integer factors of 7224 that divides 7209 without a remainder.

1, 2, 3, 4, 6, 7, 8, 12, 14, 21, 24, 28, 42, 43, 56, 84, 86, 129, 168, 172, 258, 301, 344, 516, 602, 903, 1032, 1204, 1806, 2408, 3612

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 7209 and 7224. The biggest common factor number is the GCF number.
So the greatest common factor 7209 and 7224 is 3.

Also check out the Least Common Multiple of 7209 and 7224