What is the Greatest Common Factor of 12225 and 12240?

Greatest common factor (GCF) of 12225 and 12240 is 15.

GCF(12225,12240) = 15

We will now calculate the prime factors of 12225 and 12240, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 12225 and 12240.

How to find the GCF of 12225 and 12240?

We will first find the prime factorization of 12225 and 12240. After we will calculate the factors of 12225 and 12240 and find the biggest common factor number .

Step-1: Prime Factorization of 12225

Prime factors of 12225 are 3, 5, 163. Prime factorization of 12225 in exponential form is:

12225 = 3¹ × 5² × 163¹

Step-2: Prime Factorization of 12240

Prime factors of 12240 are 2, 3, 5, 17. Prime factorization of 12240 in exponential form is:

12240 = 2⁴ × 3² × 5¹ × 17¹

Step-3: Factors of 12225

List of positive integer factors of 12225 that divides 12225 without a remainder.

1, 3, 5, 15, 25, 75, 163, 489, 815, 2445, 4075

Step-4: Factors of 12240

List of positive integer factors of 12240 that divides 12225 without a remainder.

1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 17, 18, 20, 24, 30, 34, 36, 40, 45, 48, 51, 60, 68, 72, 80, 85, 90, 102, 120, 136, 144, 153, 170, 180, 204, 240, 255, 272, 306, 340, 360, 408, 510, 612, 680, 720, 765, 816, 1020, 1224, 1360, 1530, 2040, 2448, 3060, 4080, 6120

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 12225 and 12240. The biggest common factor number is the GCF number.
So the greatest common factor 12225 and 12240 is 15.

Also check out the Least Common Multiple of 12225 and 12240