What is the Greatest Common Factor of 12838 and 12852?

Greatest common factor (GCF) of 12838 and 12852 is 14.

GCF(12838,12852) = 14

We will now calculate the prime factors of 12838 and 12852, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 12838 and 12852.

How to find the GCF of 12838 and 12852?

We will first find the prime factorization of 12838 and 12852. After we will calculate the factors of 12838 and 12852 and find the biggest common factor number .

Step-1: Prime Factorization of 12838

Prime factors of 12838 are 2, 7, 131. Prime factorization of 12838 in exponential form is:

12838 = 2¹ × 7² × 131¹

Step-2: Prime Factorization of 12852

Prime factors of 12852 are 2, 3, 7, 17. Prime factorization of 12852 in exponential form is:

12852 = 2² × 3³ × 7¹ × 17¹

Step-3: Factors of 12838

List of positive integer factors of 12838 that divides 12838 without a remainder.

1, 2, 7, 14, 49, 98, 131, 262, 917, 1834, 6419

Step-4: Factors of 12852

List of positive integer factors of 12852 that divides 12838 without a remainder.

1, 2, 3, 4, 6, 7, 9, 12, 14, 17, 18, 21, 27, 28, 34, 36, 42, 51, 54, 63, 68, 84, 102, 108, 119, 126, 153, 189, 204, 238, 252, 306, 357, 378, 459, 476, 612, 714, 756, 918, 1071, 1428, 1836, 2142, 3213, 4284, 6426

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 12838 and 12852. The biggest common factor number is the GCF number.
So the greatest common factor 12838 and 12852 is 14.

Also check out the Least Common Multiple of 12838 and 12852