What is the Greatest Common Factor of 19800 and 19817?

Greatest common factor (GCF) of 19800 and 19817 is 1.

GCF(19800,19817) = 1

We will now calculate the prime factors of 19800 and 19817, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 19800 and 19817.

How to find the GCF of 19800 and 19817?

We will first find the prime factorization of 19800 and 19817. After we will calculate the factors of 19800 and 19817 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 19817

Prime factors of 19817 are 7, 19, 149. Prime factorization of 19817 in exponential form is:

19817 = 7¹ × 19¹ × 149¹

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 19817

List of positive integer factors of 19817 that divides 19800 without a remainder.

1, 7, 19, 133, 149, 1043, 2831

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 19800 and 19817. The biggest common factor number is the GCF number.
So the greatest common factor 19800 and 19817 is 1.

Also check out the Least Common Multiple of 19800 and 19817