What is the Greatest Common Factor of 19800 and 19815?

Greatest common factor (GCF) of 19800 and 19815 is 15.

GCF(19800,19815) = 15

We will now calculate the prime factors of 19800 and 19815, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 19800 and 19815.

How to find the GCF of 19800 and 19815?

We will first find the prime factorization of 19800 and 19815. After we will calculate the factors of 19800 and 19815 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 19815

Prime factors of 19815 are 3, 5, 1321. Prime factorization of 19815 in exponential form is:

19815 = 3¹ × 5¹ × 1321¹

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 19815

List of positive integer factors of 19815 that divides 19800 without a remainder.

1, 3, 5, 15, 1321, 3963, 6605

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 19800 and 19815. The biggest common factor number is the GCF number.
So the greatest common factor 19800 and 19815 is 15.

Also check out the Least Common Multiple of 19800 and 19815