What is the Greatest Common Factor of 14189 and 14208?

Greatest common factor (GCF) of 14189 and 14208 is 1.

GCF(14189,14208) = 1

We will now calculate the prime factors of 14189 and 14208, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 14189 and 14208.

How to find the GCF of 14189 and 14208?

We will first find the prime factorization of 14189 and 14208. After we will calculate the factors of 14189 and 14208 and find the biggest common factor number .

Step-1: Prime Factorization of 14189

Prime factors of 14189 are 7, 2027. Prime factorization of 14189 in exponential form is:

14189 = 7¹ × 2027¹

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 14189

List of positive integer factors of 14189 that divides 14189 without a remainder.

1, 7, 2027

Step-4: Factors of 14208

List of positive integer factors of 14208 that divides 14189 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 14189 and 14208. The biggest common factor number is the GCF number.
So the greatest common factor 14189 and 14208 is 1.

Also check out the Least Common Multiple of 14189 and 14208