What is the Greatest Common Factor of 19800 and 19812?

Greatest common factor (GCF) of 19800 and 19812 is 12.

GCF(19800,19812) = 12

We will now calculate the prime factors of 19800 and 19812, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 19800 and 19812.

How to find the GCF of 19800 and 19812?

We will first find the prime factorization of 19800 and 19812. After we will calculate the factors of 19800 and 19812 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 19812

Prime factors of 19812 are 2, 3, 13, 127. Prime factorization of 19812 in exponential form is:

19812 = 2² × 3¹ × 13¹ × 127¹

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 19812

List of positive integer factors of 19812 that divides 19800 without a remainder.

1, 2, 3, 4, 6, 12, 13, 26, 39, 52, 78, 127, 156, 254, 381, 508, 762, 1524, 1651, 3302, 4953, 6604, 9906

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 19800 and 19812. The biggest common factor number is the GCF number.
So the greatest common factor 19800 and 19812 is 12.

Also check out the Least Common Multiple of 19800 and 19812