What is the Greatest Common Factor of 76800 and 76812?

Greatest common factor (GCF) of 76800 and 76812 is 12.

GCF(76800,76812) = 12

We will now calculate the prime factors of 76800 and 76812, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 76800 and 76812.

How to find the GCF of 76800 and 76812?

We will first find the prime factorization of 76800 and 76812. After we will calculate the factors of 76800 and 76812 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 76812

Prime factors of 76812 are 2, 3, 37, 173. Prime factorization of 76812 in exponential form is:

76812 = 2² × 3¹ × 37¹ × 173¹

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 76812

List of positive integer factors of 76812 that divides 76800 without a remainder.

1, 2, 3, 4, 6, 12, 37, 74, 111, 148, 173, 222, 346, 444, 519, 692, 1038, 2076, 6401, 12802, 19203, 25604, 38406

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 76800 and 76812. The biggest common factor number is the GCF number.
So the greatest common factor 76800 and 76812 is 12.

Also check out the Least Common Multiple of 76800 and 76812