What is the Greatest Common Factor of 14204 and 14224?

Greatest common factor (GCF) of 14204 and 14224 is 4.

GCF(14204,14224) = 4

We will now calculate the prime factors of 14204 and 14224, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 14204 and 14224.

How to find the GCF of 14204 and 14224?

We will first find the prime factorization of 14204 and 14224. After we will calculate the factors of 14204 and 14224 and find the biggest common factor number .

Step-1: Prime Factorization of 14204

Prime factors of 14204 are 2, 53, 67. Prime factorization of 14204 in exponential form is:

14204 = 2² × 53¹ × 67¹

Step-2: Prime Factorization of 14224

Prime factors of 14224 are 2, 7, 127. Prime factorization of 14224 in exponential form is:

14224 = 2⁴ × 7¹ × 127¹

Step-3: Factors of 14204

List of positive integer factors of 14204 that divides 14204 without a remainder.

1, 2, 4, 53, 67, 106, 134, 212, 268, 3551, 7102

Step-4: Factors of 14224

List of positive integer factors of 14224 that divides 14204 without a remainder.

1, 2, 4, 7, 8, 14, 16, 28, 56, 112, 127, 254, 508, 889, 1016, 1778, 2032, 3556, 7112

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 14204 and 14224. The biggest common factor number is the GCF number.
So the greatest common factor 14204 and 14224 is 4.

Also check out the Least Common Multiple of 14204 and 14224