What is the Greatest Common Factor of 16185 and 16200?

Greatest common factor (GCF) of 16185 and 16200 is 15.

GCF(16185,16200) = 15

We will now calculate the prime factors of 16185 and 16200, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 16185 and 16200.

How to find the GCF of 16185 and 16200?

We will first find the prime factorization of 16185 and 16200. After we will calculate the factors of 16185 and 16200 and find the biggest common factor number .

Step-1: Prime Factorization of 16185

Prime factors of 16185 are 3, 5, 13, 83. Prime factorization of 16185 in exponential form is:

16185 = 3¹ × 5¹ × 13¹ × 83¹

Step-2: 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-3: Factors of 16185

List of positive integer factors of 16185 that divides 16185 without a remainder.

1, 3, 5, 13, 15, 39, 65, 83, 195, 249, 415, 1079, 1245, 3237, 5395

Step-4: Factors of 16200

List of positive integer factors of 16200 that divides 16185 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 16185 and 16200. The biggest common factor number is the GCF number.
So the greatest common factor 16185 and 16200 is 15.

Also check out the Least Common Multiple of 16185 and 16200