What is the Greatest Common Factor of 19785 and 19800?

Greatest common factor (GCF) of 19785 and 19800 is 15.

GCF(19785,19800) = 15

We will now calculate the prime factors of 19785 and 19800, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 19785 and 19800.

How to find the GCF of 19785 and 19800?

We will first find the prime factorization of 19785 and 19800. After we will calculate the factors of 19785 and 19800 and find the biggest common factor number .

Step-1: Prime Factorization of 19785

Prime factors of 19785 are 3, 5, 1319. Prime factorization of 19785 in exponential form is:

19785 = 3¹ × 5¹ × 1319¹

Step-2: 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-3: Factors of 19785

List of positive integer factors of 19785 that divides 19785 without a remainder.

1, 3, 5, 15, 1319, 3957, 6595

Step-4: Factors of 19800

List of positive integer factors of 19800 that divides 19785 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 19785 and 19800. The biggest common factor number is the GCF number.
So the greatest common factor 19785 and 19800 is 15.

Also check out the Least Common Multiple of 19785 and 19800