What is the Greatest Common Factor of 19789 and 19800?

Greatest common factor (GCF) of 19789 and 19800 is 11.

GCF(19789,19800) = 11

We will now calculate the prime factors of 19789 and 19800, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 19789 and 19800.

How to find the GCF of 19789 and 19800?

We will first find the prime factorization of 19789 and 19800. After we will calculate the factors of 19789 and 19800 and find the biggest common factor number .

Step-1: Prime Factorization of 19789

Prime factors of 19789 are 7, 11, 257. Prime factorization of 19789 in exponential form is:

19789 = 7¹ × 11¹ × 257¹

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 19789

List of positive integer factors of 19789 that divides 19789 without a remainder.

1, 7, 11, 77, 257, 1799, 2827

Step-4: Factors of 19800

List of positive integer factors of 19800 that divides 19789 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 19789 and 19800. The biggest common factor number is the GCF number.
So the greatest common factor 19789 and 19800 is 11.

Also check out the Least Common Multiple of 19789 and 19800