What is the Greatest Common Factor of 6783 and 6800?

Greatest common factor (GCF) of 6783 and 6800 is 17.

GCF(6783,6800) = 17

We will now calculate the prime factors of 6783 and 6800, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 6783 and 6800.

How to find the GCF of 6783 and 6800?

We will first find the prime factorization of 6783 and 6800. After we will calculate the factors of 6783 and 6800 and find the biggest common factor number .

Step-1: Prime Factorization of 6783

Prime factors of 6783 are 3, 7, 17, 19. Prime factorization of 6783 in exponential form is:

6783 = 3¹ × 7¹ × 17¹ × 19¹

Step-2: Prime Factorization of 6800

Prime factors of 6800 are 2, 5, 17. Prime factorization of 6800 in exponential form is:

6800 = 2⁴ × 5² × 17¹

Step-3: Factors of 6783

List of positive integer factors of 6783 that divides 6783 without a remainder.

1, 3, 7, 17, 19, 21, 51, 57, 119, 133, 323, 357, 399, 969, 2261

Step-4: Factors of 6800

List of positive integer factors of 6800 that divides 6783 without a remainder.

1, 2, 4, 5, 8, 10, 16, 17, 20, 25, 34, 40, 50, 68, 80, 85, 100, 136, 170, 200, 272, 340, 400, 425, 680, 850, 1360, 1700, 3400

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 6783 and 6800. The biggest common factor number is the GCF number.
So the greatest common factor 6783 and 6800 is 17.

Also check out the Least Common Multiple of 6783 and 6800