What is the Greatest Common Factor of 14196 and 14208?

Greatest common factor (GCF) of 14196 and 14208 is 12.

GCF(14196,14208) = 12

We will now calculate the prime factors of 14196 and 14208, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 14196 and 14208.

How to find the GCF of 14196 and 14208?

We will first find the prime factorization of 14196 and 14208. After we will calculate the factors of 14196 and 14208 and find the biggest common factor number .

Step-1: Prime Factorization of 14196

Prime factors of 14196 are 2, 3, 7, 13. Prime factorization of 14196 in exponential form is:

14196 = 2² × 3¹ × 7¹ × 13²

Step-2: Prime Factorization of 14208

Prime factors of 14208 are 2, 3, 37. Prime factorization of 14208 in exponential form is:

14208 = 2⁷ × 3¹ × 37¹

Step-3: Factors of 14196

List of positive integer factors of 14196 that divides 14196 without a remainder.

1, 2, 3, 4, 6, 7, 12, 13, 14, 21, 26, 28, 39, 42, 52, 78, 84, 91, 156, 169, 182, 273, 338, 364, 507, 546, 676, 1014, 1092, 1183, 2028, 2366, 3549, 4732, 7098

Step-4: Factors of 14208

List of positive integer factors of 14208 that divides 14196 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 37, 48, 64, 74, 96, 111, 128, 148, 192, 222, 296, 384, 444, 592, 888, 1184, 1776, 2368, 3552, 4736, 7104

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 14196 and 14208. The biggest common factor number is the GCF number.
So the greatest common factor 14196 and 14208 is 12.

Also check out the Least Common Multiple of 14196 and 14208