What is the Greatest Common Factor of 30789 and 30800?

Greatest common factor (GCF) of 30789 and 30800 is 11.

GCF(30789,30800) = 11

We will now calculate the prime factors of 30789 and 30800, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 30789 and 30800.

How to find the GCF of 30789 and 30800?

We will first find the prime factorization of 30789 and 30800. After we will calculate the factors of 30789 and 30800 and find the biggest common factor number .

Step-1: Prime Factorization of 30789

Prime factors of 30789 are 3, 11, 311. Prime factorization of 30789 in exponential form is:

30789 = 3² × 11¹ × 311¹

Step-2: Prime Factorization of 30800

Prime factors of 30800 are 2, 5, 7, 11. Prime factorization of 30800 in exponential form is:

30800 = 2⁴ × 5² × 7¹ × 11¹

Step-3: Factors of 30789

List of positive integer factors of 30789 that divides 30789 without a remainder.

1, 3, 9, 11, 33, 99, 311, 933, 2799, 3421, 10263

Step-4: Factors of 30800

List of positive integer factors of 30800 that divides 30789 without a remainder.

1, 2, 4, 5, 7, 8, 10, 11, 14, 16, 20, 22, 25, 28, 35, 40, 44, 50, 55, 56, 70, 77, 80, 88, 100, 110, 112, 140, 154, 175, 176, 200, 220, 275, 280, 308, 350, 385, 400, 440, 550, 560, 616, 700, 770, 880, 1100, 1232, 1400, 1540, 1925, 2200, 2800, 3080, 3850, 4400, 6160, 7700, 15400

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 30789 and 30800. The biggest common factor number is the GCF number.
So the greatest common factor 30789 and 30800 is 11.

Also check out the Least Common Multiple of 30789 and 30800