What is the Greatest Common Factor of 18214 and 18224?

Greatest common factor (GCF) of 18214 and 18224 is 2.

GCF(18214,18224) = 2

We will now calculate the prime factors of 18214 and 18224, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 18214 and 18224.

How to find the GCF of 18214 and 18224?

We will first find the prime factorization of 18214 and 18224. After we will calculate the factors of 18214 and 18224 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 18224

Prime factors of 18224 are 2, 17, 67. Prime factorization of 18224 in exponential form is:

18224 = 2⁴ × 17¹ × 67¹

Step-3: Factors of 18214

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

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

Step-4: Factors of 18224

List of positive integer factors of 18224 that divides 18214 without a remainder.

1, 2, 4, 8, 16, 17, 34, 67, 68, 134, 136, 268, 272, 536, 1072, 1139, 2278, 4556, 9112

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 18214 and 18224. The biggest common factor number is the GCF number.
So the greatest common factor 18214 and 18224 is 2.

Also check out the Least Common Multiple of 18214 and 18224