What is the Greatest Common Factor of 10800 and 10819?

Greatest common factor (GCF) of 10800 and 10819 is 1.

GCF(10800,10819) = 1

We will now calculate the prime factors of 10800 and 10819, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 10800 and 10819.

How to find the GCF of 10800 and 10819?

We will first find the prime factorization of 10800 and 10819. After we will calculate the factors of 10800 and 10819 and find the biggest common factor number .

Step-1: Prime Factorization of 10800

Prime factors of 10800 are 2, 3, 5. Prime factorization of 10800 in exponential form is:

10800 = 2⁴ × 3³ × 5²

Step-2: Prime Factorization of 10819

Prime factors of 10819 are 31, 349. Prime factorization of 10819 in exponential form is:

10819 = 31¹ × 349¹

Step-3: Factors of 10800

List of positive integer factors of 10800 that divides 10800 without a remainder.

1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 25, 27, 30, 36, 40, 45, 48, 50, 54, 60, 72, 75, 80, 90, 100, 108, 120, 135, 144, 150, 180, 200, 216, 225, 240, 270, 300, 360, 400, 432, 450, 540, 600, 675, 720, 900, 1080, 1200, 1350, 1800, 2160, 2700, 3600, 5400

Step-4: Factors of 10819

List of positive integer factors of 10819 that divides 10800 without a remainder.

1, 31, 349

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 10800 and 10819. The biggest common factor number is the GCF number.
So the greatest common factor 10800 and 10819 is 1.

Also check out the Least Common Multiple of 10800 and 10819