What is the Greatest Common Factor of 16782 and 16800?

Greatest common factor (GCF) of 16782 and 16800 is 6.

GCF(16782,16800) = 6

We will now calculate the prime factors of 16782 and 16800, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 16782 and 16800.

How to find the GCF of 16782 and 16800?

We will first find the prime factorization of 16782 and 16800. After we will calculate the factors of 16782 and 16800 and find the biggest common factor number .

Step-1: Prime Factorization of 16782

Prime factors of 16782 are 2, 3, 2797. Prime factorization of 16782 in exponential form is:

16782 = 2¹ × 3¹ × 2797¹

Step-2: 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-3: Factors of 16782

List of positive integer factors of 16782 that divides 16782 without a remainder.

1, 2, 3, 6, 2797, 5594, 8391

Step-4: Factors of 16800

List of positive integer factors of 16800 that divides 16782 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 16782 and 16800. The biggest common factor number is the GCF number.
So the greatest common factor 16782 and 16800 is 6.

Also check out the Least Common Multiple of 16782 and 16800