What is the Greatest Common Factor of 13800 and 13810?

Greatest common factor (GCF) of 13800 and 13810 is 10.

GCF(13800,13810) = 10

We will now calculate the prime factors of 13800 and 13810, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 13800 and 13810.

How to find the GCF of 13800 and 13810?

We will first find the prime factorization of 13800 and 13810. After we will calculate the factors of 13800 and 13810 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 13810

Prime factors of 13810 are 2, 5, 1381. Prime factorization of 13810 in exponential form is:

13810 = 2¹ × 5¹ × 1381¹

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 13810

List of positive integer factors of 13810 that divides 13800 without a remainder.

1, 2, 5, 10, 1381, 2762, 6905

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 13800 and 13810. The biggest common factor number is the GCF number.
So the greatest common factor 13800 and 13810 is 10.

Also check out the Least Common Multiple of 13800 and 13810