What is the Greatest Common Factor of 76800 and 76807?

Greatest common factor (GCF) of 76800 and 76807 is 1.

GCF(76800,76807) = 1

We will now calculate the prime factors of 76800 and 76807, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 76800 and 76807.

How to find the GCF of 76800 and 76807?

We will first find the prime factorization of 76800 and 76807. After we will calculate the factors of 76800 and 76807 and find the biggest common factor number .

Step-1: Prime Factorization of 76800

Prime factors of 76800 are 2, 3, 5. Prime factorization of 76800 in exponential form is:

76800 = 2¹⁰ × 3¹ × 5²

Step-2: Prime Factorization of 76807

Prime factors of 76807 are 89, 863. Prime factorization of 76807 in exponential form is:

76807 = 89¹ × 863¹

Step-3: Factors of 76800

List of positive integer factors of 76800 that divides 76800 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 25, 30, 32, 40, 48, 50, 60, 64, 75, 80, 96, 100, 120, 128, 150, 160, 192, 200, 240, 256, 300, 320, 384, 400, 480, 512, 600, 640, 768, 800, 960, 1024, 1200, 1280, 1536, 1600, 1920, 2400, 2560, 3072, 3200, 3840, 4800, 5120, 6400, 7680, 9600, 12800, 15360, 19200, 25600, 38400

Step-4: Factors of 76807

List of positive integer factors of 76807 that divides 76800 without a remainder.

1, 89, 863

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 76800 and 76807. The biggest common factor number is the GCF number.
So the greatest common factor 76800 and 76807 is 1.

Also check out the Least Common Multiple of 76800 and 76807