What is the Greatest Common Factor of 18200 and 18214?

Greatest common factor (GCF) of 18200 and 18214 is 14.

GCF(18200,18214) = 14

We will now calculate the prime factors of 18200 and 18214, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 18200 and 18214.

How to find the GCF of 18200 and 18214?

We will first find the prime factorization of 18200 and 18214. After we will calculate the factors of 18200 and 18214 and find the biggest common factor number .

Step-1: Prime Factorization of 18200

Prime factors of 18200 are 2, 5, 7, 13. Prime factorization of 18200 in exponential form is:

18200 = 2³ × 5² × 7¹ × 13¹

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 18200

List of positive integer factors of 18200 that divides 18200 without a remainder.

1, 2, 4, 5, 7, 8, 10, 13, 14, 20, 25, 26, 28, 35, 40, 50, 52, 56, 65, 70, 91, 100, 104, 130, 140, 175, 182, 200, 260, 280, 325, 350, 364, 455, 520, 650, 700, 728, 910, 1300, 1400, 1820, 2275, 2600, 3640, 4550, 9100

Step-4: Factors of 18214

List of positive integer factors of 18214 that divides 18200 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 18200 and 18214. The biggest common factor number is the GCF number.
So the greatest common factor 18200 and 18214 is 14.

Also check out the Least Common Multiple of 18200 and 18214