What is the Greatest Common Factor of 13782 and 13800?

Greatest common factor (GCF) of 13782 and 13800 is 6.

GCF(13782,13800) = 6

We will now calculate the prime factors of 13782 and 13800, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 13782 and 13800.

How to find the GCF of 13782 and 13800?

We will first find the prime factorization of 13782 and 13800. After we will calculate the factors of 13782 and 13800 and find the biggest common factor number .

Step-1: Prime Factorization of 13782

Prime factors of 13782 are 2, 3, 2297. Prime factorization of 13782 in exponential form is:

13782 = 2¹ × 3¹ × 2297¹

Step-2: Prime Factorization of 13800

Prime factors of 13800 are 2, 3, 5, 23. Prime factorization of 13800 in exponential form is:

13800 = 2³ × 3¹ × 5² × 23¹

Step-3: Factors of 13782

List of positive integer factors of 13782 that divides 13782 without a remainder.

1, 2, 3, 6, 2297, 4594, 6891

Step-4: Factors of 13800

List of positive integer factors of 13800 that divides 13782 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 23, 24, 25, 30, 40, 46, 50, 60, 69, 75, 92, 100, 115, 120, 138, 150, 184, 200, 230, 276, 300, 345, 460, 552, 575, 600, 690, 920, 1150, 1380, 1725, 2300, 2760, 3450, 4600, 6900

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 13782 and 13800. The biggest common factor number is the GCF number.
So the greatest common factor 13782 and 13800 is 6.

Also check out the Least Common Multiple of 13782 and 13800