What is the Greatest Common Factor of 16800 and 16809?

Greatest common factor (GCF) of 16800 and 16809 is 3.

GCF(16800,16809) = 3

We will now calculate the prime factors of 16800 and 16809, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 16800 and 16809.

How to find the GCF of 16800 and 16809?

We will first find the prime factorization of 16800 and 16809. After we will calculate the factors of 16800 and 16809 and find the biggest common factor number .

Step-1: Prime Factorization of 16800

Prime factors of 16800 are 2, 3, 5, 7. Prime factorization of 16800 in exponential form is:

16800 = 2⁵ × 3¹ × 5² × 7¹

Step-2: Prime Factorization of 16809

Prime factors of 16809 are 3, 13, 431. Prime factorization of 16809 in exponential form is:

16809 = 3¹ × 13¹ × 431¹

Step-3: Factors of 16800

List of positive integer factors of 16800 that divides 16800 without a remainder.

1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 16, 20, 21, 24, 25, 28, 30, 32, 35, 40, 42, 48, 50, 56, 60, 70, 75, 80, 84, 96, 100, 105, 112, 120, 140, 150, 160, 168, 175, 200, 210, 224, 240, 280, 300, 336, 350, 400, 420, 480, 525, 560, 600, 672, 700, 800, 840, 1050, 1120, 1200, 1400, 1680, 2100, 2400, 2800, 3360, 4200, 5600, 8400

Step-4: Factors of 16809

List of positive integer factors of 16809 that divides 16800 without a remainder.

1, 3, 13, 39, 431, 1293, 5603

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 16800 and 16809. The biggest common factor number is the GCF number.
So the greatest common factor 16800 and 16809 is 3.

Also check out the Least Common Multiple of 16800 and 16809