What is the Greatest Common Factor of 76800 and 76816?

Greatest common factor (GCF) of 76800 and 76816 is 16.

GCF(76800,76816) = 16

We will now calculate the prime factors of 76800 and 76816, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 76800 and 76816.

How to find the GCF of 76800 and 76816?

We will first find the prime factorization of 76800 and 76816. After we will calculate the factors of 76800 and 76816 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 76816

Prime factors of 76816 are 2, 4801. Prime factorization of 76816 in exponential form is:

76816 = 2⁴ × 4801¹

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 76816

List of positive integer factors of 76816 that divides 76800 without a remainder.

1, 2, 4, 8, 16, 4801, 9602, 19204, 38408

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 76800 and 76816. The biggest common factor number is the GCF number.
So the greatest common factor 76800 and 76816 is 16.

Also check out the Least Common Multiple of 76800 and 76816