What is the Greatest Common Factor of 14208 and 14219?

Greatest common factor (GCF) of 14208 and 14219 is 1.

GCF(14208,14219) = 1

We will now calculate the prime factors of 14208 and 14219, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 14208 and 14219.

How to find the GCF of 14208 and 14219?

We will first find the prime factorization of 14208 and 14219. After we will calculate the factors of 14208 and 14219 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 14219

Prime factors of 14219 are 59, 241. Prime factorization of 14219 in exponential form is:

14219 = 59¹ × 241¹

Step-3: Factors of 14208

List of positive integer factors of 14208 that divides 14208 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

Step-4: Factors of 14219

List of positive integer factors of 14219 that divides 14208 without a remainder.

1, 59, 241

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 14208 and 14219. The biggest common factor number is the GCF number.
So the greatest common factor 14208 and 14219 is 1.

Also check out the Least Common Multiple of 14208 and 14219