What is the Greatest Common Factor of 13800 and 13806?

Greatest common factor (GCF) of 13800 and 13806 is 6.

GCF(13800,13806) = 6

We will now calculate the prime factors of 13800 and 13806, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 13800 and 13806.

How to find the GCF of 13800 and 13806?

We will first find the prime factorization of 13800 and 13806. After we will calculate the factors of 13800 and 13806 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 13806

Prime factors of 13806 are 2, 3, 13, 59. Prime factorization of 13806 in exponential form is:

13806 = 2¹ × 3² × 13¹ × 59¹

Step-3: Factors of 13800

List of positive integer factors of 13800 that divides 13800 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

Step-4: Factors of 13806

List of positive integer factors of 13806 that divides 13800 without a remainder.

1, 2, 3, 6, 9, 13, 18, 26, 39, 59, 78, 117, 118, 177, 234, 354, 531, 767, 1062, 1534, 2301, 4602, 6903

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 13800 and 13806. The biggest common factor number is the GCF number.
So the greatest common factor 13800 and 13806 is 6.

Also check out the Least Common Multiple of 13800 and 13806