What is the Greatest Common Factor of 16200 and 16214?

Greatest common factor (GCF) of 16200 and 16214 is 2.

GCF(16200,16214) = 2

We will now calculate the prime factors of 16200 and 16214, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 16200 and 16214.

How to find the GCF of 16200 and 16214?

We will first find the prime factorization of 16200 and 16214. After we will calculate the factors of 16200 and 16214 and find the biggest common factor number .

Step-1: Prime Factorization of 16200

Prime factors of 16200 are 2, 3, 5. Prime factorization of 16200 in exponential form is:

16200 = 2³ × 3⁴ × 5²

Step-2: Prime Factorization of 16214

Prime factors of 16214 are 2, 11, 67. Prime factorization of 16214 in exponential form is:

16214 = 2¹ × 11² × 67¹

Step-3: Factors of 16200

List of positive integer factors of 16200 that divides 16200 without a remainder.

1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 25, 27, 30, 36, 40, 45, 50, 54, 60, 72, 75, 81, 90, 100, 108, 120, 135, 150, 162, 180, 200, 216, 225, 270, 300, 324, 360, 405, 450, 540, 600, 648, 675, 810, 900, 1080, 1350, 1620, 1800, 2025, 2700, 3240, 4050, 5400, 8100

Step-4: Factors of 16214

List of positive integer factors of 16214 that divides 16200 without a remainder.

1, 2, 11, 22, 67, 121, 134, 242, 737, 1474, 8107

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 16200 and 16214. The biggest common factor number is the GCF number.
So the greatest common factor 16200 and 16214 is 2.

Also check out the Least Common Multiple of 16200 and 16214