What is the Greatest Common Factor of 76800 and 76820?

Greatest common factor (GCF) of 76800 and 76820 is 20.

GCF(76800,76820) = 20

We will now calculate the prime factors of 76800 and 76820, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 76800 and 76820.

How to find the GCF of 76800 and 76820?

We will first find the prime factorization of 76800 and 76820. After we will calculate the factors of 76800 and 76820 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 76820

Prime factors of 76820 are 2, 5, 23, 167. Prime factorization of 76820 in exponential form is:

76820 = 2² × 5¹ × 23¹ × 167¹

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 76820

List of positive integer factors of 76820 that divides 76800 without a remainder.

1, 2, 4, 5, 10, 20, 23, 46, 92, 115, 167, 230, 334, 460, 668, 835, 1670, 3340, 3841, 7682, 15364, 19205, 38410

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 76800 and 76820. The biggest common factor number is the GCF number.
So the greatest common factor 76800 and 76820 is 20.

Also check out the Least Common Multiple of 76800 and 76820