What is the Greatest Common Factor of 14256 and 14274?

Greatest common factor (GCF) of 14256 and 14274 is 18.

GCF(14256,14274) = 18

We will now calculate the prime factors of 14256 and 14274, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 14256 and 14274.

How to find the GCF of 14256 and 14274?

We will first find the prime factorization of 14256 and 14274. After we will calculate the factors of 14256 and 14274 and find the biggest common factor number .

Step-1: Prime Factorization of 14256

Prime factors of 14256 are 2, 3, 11. Prime factorization of 14256 in exponential form is:

14256 = 2⁴ × 3⁴ × 11¹

Step-2: Prime Factorization of 14274

Prime factors of 14274 are 2, 3, 13, 61. Prime factorization of 14274 in exponential form is:

14274 = 2¹ × 3² × 13¹ × 61¹

Step-3: Factors of 14256

List of positive integer factors of 14256 that divides 14256 without a remainder.

1, 2, 3, 4, 6, 8, 9, 11, 12, 16, 18, 22, 24, 27, 33, 36, 44, 48, 54, 66, 72, 81, 88, 99, 108, 132, 144, 162, 176, 198, 216, 264, 297, 324, 396, 432, 528, 594, 648, 792, 891, 1188, 1296, 1584, 1782, 2376, 3564, 4752, 7128

Step-4: Factors of 14274

List of positive integer factors of 14274 that divides 14256 without a remainder.

1, 2, 3, 6, 9, 13, 18, 26, 39, 61, 78, 117, 122, 183, 234, 366, 549, 793, 1098, 1586, 2379, 4758, 7137

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 14256 and 14274. The biggest common factor number is the GCF number.
So the greatest common factor 14256 and 14274 is 18.

Also check out the Least Common Multiple of 14256 and 14274