What is the Greatest Common Factor of 10800 and 10814?

Greatest common factor (GCF) of 10800 and 10814 is 2.

GCF(10800,10814) = 2

We will now calculate the prime factors of 10800 and 10814, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 10800 and 10814.

How to find the GCF of 10800 and 10814?

We will first find the prime factorization of 10800 and 10814. After we will calculate the factors of 10800 and 10814 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 10814

Prime factors of 10814 are 2, 5407. Prime factorization of 10814 in exponential form is:

10814 = 2¹ × 5407¹

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 10814

List of positive integer factors of 10814 that divides 10800 without a remainder.

1, 2, 5407

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 10800 and 10814. The biggest common factor number is the GCF number.
So the greatest common factor 10800 and 10814 is 2.

Also check out the Least Common Multiple of 10800 and 10814