What is the Greatest Common Factor of 16800 and 16814?

Greatest common factor (GCF) of 16800 and 16814 is 14.

GCF(16800,16814) = 14

We will now calculate the prime factors of 16800 and 16814, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 16800 and 16814.

How to find the GCF of 16800 and 16814?

We will first find the prime factorization of 16800 and 16814. After we will calculate the factors of 16800 and 16814 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 16814

Prime factors of 16814 are 2, 7, 1201. Prime factorization of 16814 in exponential form is:

16814 = 2¹ × 7¹ × 1201¹

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 16814

List of positive integer factors of 16814 that divides 16800 without a remainder.

1, 2, 7, 14, 1201, 2402, 8407

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 16800 and 16814. The biggest common factor number is the GCF number.
So the greatest common factor 16800 and 16814 is 14.

Also check out the Least Common Multiple of 16800 and 16814