What is the Greatest Common Factor of 12240 and 12257?

Greatest common factor (GCF) of 12240 and 12257 is 17.

GCF(12240,12257) = 17

We will now calculate the prime factors of 12240 and 12257, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 12240 and 12257.

How to find the GCF of 12240 and 12257?

We will first find the prime factorization of 12240 and 12257. After we will calculate the factors of 12240 and 12257 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 12257

Prime factors of 12257 are 7, 17, 103. Prime factorization of 12257 in exponential form is:

12257 = 7¹ × 17¹ × 103¹

Step-3: Factors of 12240

List of positive integer factors of 12240 that divides 12240 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

Step-4: Factors of 12257

List of positive integer factors of 12257 that divides 12240 without a remainder.

1, 7, 17, 103, 119, 721, 1751

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 12240 and 12257. The biggest common factor number is the GCF number.
So the greatest common factor 12240 and 12257 is 17.

Also check out the Least Common Multiple of 12240 and 12257