What is the Greatest Common Factor of 12259 and 12272?

Greatest common factor (GCF) of 12259 and 12272 is 13.

GCF(12259,12272) = 13

We will now calculate the prime factors of 12259 and 12272, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 12259 and 12272.

How to find the GCF of 12259 and 12272?

We will first find the prime factorization of 12259 and 12272. After we will calculate the factors of 12259 and 12272 and find the biggest common factor number .

Step-1: Prime Factorization of 12259

Prime factors of 12259 are 13, 23, 41. Prime factorization of 12259 in exponential form is:

12259 = 13¹ × 23¹ × 41¹

Step-2: Prime Factorization of 12272

Prime factors of 12272 are 2, 13, 59. Prime factorization of 12272 in exponential form is:

12272 = 2⁴ × 13¹ × 59¹

Step-3: Factors of 12259

List of positive integer factors of 12259 that divides 12259 without a remainder.

1, 13, 23, 41, 299, 533, 943

Step-4: Factors of 12272

List of positive integer factors of 12272 that divides 12259 without a remainder.

1, 2, 4, 8, 13, 16, 26, 52, 59, 104, 118, 208, 236, 472, 767, 944, 1534, 3068, 6136

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 12259 and 12272. The biggest common factor number is the GCF number.
So the greatest common factor 12259 and 12272 is 13.

Also check out the Least Common Multiple of 12259 and 12272