What is the Greatest Common Factor of 19800 and 19809?

Greatest common factor (GCF) of 19800 and 19809 is 9.

GCF(19800,19809) = 9

We will now calculate the prime factors of 19800 and 19809, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 19800 and 19809.

How to find the GCF of 19800 and 19809?

We will first find the prime factorization of 19800 and 19809. After we will calculate the factors of 19800 and 19809 and find the biggest common factor number .

Step-1: Prime Factorization of 19800

Prime factors of 19800 are 2, 3, 5, 11. Prime factorization of 19800 in exponential form is:

19800 = 2³ × 3² × 5² × 11¹

Step-2: Prime Factorization of 19809

Prime factors of 19809 are 3, 31, 71. Prime factorization of 19809 in exponential form is:

19809 = 3² × 31¹ × 71¹

Step-3: Factors of 19800

List of positive integer factors of 19800 that divides 19800 without a remainder.

1, 2, 3, 4, 5, 6, 8, 9, 10, 11, 12, 15, 18, 20, 22, 24, 25, 30, 33, 36, 40, 44, 45, 50, 55, 60, 66, 72, 75, 88, 90, 99, 100, 110, 120, 132, 150, 165, 180, 198, 200, 220, 225, 264, 275, 300, 330, 360, 396, 440, 450, 495, 550, 600, 660, 792, 825, 900, 990, 1100, 1320, 1650, 1800, 1980, 2200, 2475, 3300, 3960, 4950, 6600, 9900

Step-4: Factors of 19809

List of positive integer factors of 19809 that divides 19800 without a remainder.

1, 3, 9, 31, 71, 93, 213, 279, 639, 2201, 6603

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 19800 and 19809. The biggest common factor number is the GCF number.
So the greatest common factor 19800 and 19809 is 9.

Also check out the Least Common Multiple of 19800 and 19809