What is the Greatest Common Factor of 76780 and 76800?

Greatest common factor (GCF) of 76780 and 76800 is 20.

GCF(76780,76800) = 20

We will now calculate the prime factors of 76780 and 76800, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 76780 and 76800.

How to find the GCF of 76780 and 76800?

We will first find the prime factorization of 76780 and 76800. After we will calculate the factors of 76780 and 76800 and find the biggest common factor number .

Step-1: Prime Factorization of 76780

Prime factors of 76780 are 2, 5, 11, 349. Prime factorization of 76780 in exponential form is:

76780 = 2² × 5¹ × 11¹ × 349¹

Step-2: 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-3: Factors of 76780

List of positive integer factors of 76780 that divides 76780 without a remainder.

1, 2, 4, 5, 10, 11, 20, 22, 44, 55, 110, 220, 349, 698, 1396, 1745, 3490, 3839, 6980, 7678, 15356, 19195, 38390

Step-4: Factors of 76800

List of positive integer factors of 76800 that divides 76780 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 76780 and 76800. The biggest common factor number is the GCF number.
So the greatest common factor 76780 and 76800 is 20.

Also check out the Least Common Multiple of 76780 and 76800