What is the Greatest Common Factor of 10782 and 10800?

Greatest common factor (GCF) of 10782 and 10800 is 18.

GCF(10782,10800) = 18

We will now calculate the prime factors of 10782 and 10800, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 10782 and 10800.

How to find the GCF of 10782 and 10800?

We will first find the prime factorization of 10782 and 10800. After we will calculate the factors of 10782 and 10800 and find the biggest common factor number .

Step-1: Prime Factorization of 10782

Prime factors of 10782 are 2, 3, 599. Prime factorization of 10782 in exponential form is:

10782 = 2¹ × 3² × 599¹

Step-2: 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-3: Factors of 10782

List of positive integer factors of 10782 that divides 10782 without a remainder.

1, 2, 3, 6, 9, 18, 599, 1198, 1797, 3594, 5391

Step-4: Factors of 10800

List of positive integer factors of 10800 that divides 10782 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 10782 and 10800. The biggest common factor number is the GCF number.
So the greatest common factor 10782 and 10800 is 18.

Also check out the Least Common Multiple of 10782 and 10800