What is the Greatest Common Factor of 16200 and 16209?

Greatest common factor (GCF) of 16200 and 16209 is 9.

GCF(16200,16209) = 9

We will now calculate the prime factors of 16200 and 16209, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 16200 and 16209.

How to find the GCF of 16200 and 16209?

We will first find the prime factorization of 16200 and 16209. After we will calculate the factors of 16200 and 16209 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 16209

Prime factors of 16209 are 3, 1801. Prime factorization of 16209 in exponential form is:

16209 = 3² × 1801¹

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 16209

List of positive integer factors of 16209 that divides 16200 without a remainder.

1, 3, 9, 1801, 5403

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 16200 and 16209. The biggest common factor number is the GCF number.
So the greatest common factor 16200 and 16209 is 9.

Also check out the Least Common Multiple of 16200 and 16209