What is the Greatest Common Factor of 18208 and 18214?

Greatest common factor (GCF) of 18208 and 18214 is 2.

GCF(18208,18214) = 2

We will now calculate the prime factors of 18208 and 18214, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 18208 and 18214.

How to find the GCF of 18208 and 18214?

We will first find the prime factorization of 18208 and 18214. After we will calculate the factors of 18208 and 18214 and find the biggest common factor number .

Step-1: Prime Factorization of 18208

Prime factors of 18208 are 2, 569. Prime factorization of 18208 in exponential form is:

18208 = 2⁵ × 569¹

Step-2: Prime Factorization of 18214

Prime factors of 18214 are 2, 7, 1301. Prime factorization of 18214 in exponential form is:

18214 = 2¹ × 7¹ × 1301¹

Step-3: Factors of 18208

List of positive integer factors of 18208 that divides 18208 without a remainder.

1, 2, 4, 8, 16, 32, 569, 1138, 2276, 4552, 9104

Step-4: Factors of 18214

List of positive integer factors of 18214 that divides 18208 without a remainder.

1, 2, 7, 14, 1301, 2602, 9107

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 18208 and 18214. The biggest common factor number is the GCF number.
So the greatest common factor 18208 and 18214 is 2.

Also check out the Least Common Multiple of 18208 and 18214