What is the Greatest Common Factor of 21780 and 21800?

Greatest common factor (GCF) of 21780 and 21800 is 20.

GCF(21780,21800) = 20

We will now calculate the prime factors of 21780 and 21800, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 21780 and 21800.

How to find the GCF of 21780 and 21800?

We will first find the prime factorization of 21780 and 21800. After we will calculate the factors of 21780 and 21800 and find the biggest common factor number .

Step-1: Prime Factorization of 21780

Prime factors of 21780 are 2, 3, 5, 11. Prime factorization of 21780 in exponential form is:

21780 = 2² × 3² × 5¹ × 11²

Step-2: Prime Factorization of 21800

Prime factors of 21800 are 2, 5, 109. Prime factorization of 21800 in exponential form is:

21800 = 2³ × 5² × 109¹

Step-3: Factors of 21780

List of positive integer factors of 21780 that divides 21780 without a remainder.

1, 2, 3, 4, 5, 6, 9, 10, 11, 12, 15, 18, 20, 22, 30, 33, 36, 44, 45, 55, 60, 66, 90, 99, 110, 121, 132, 165, 180, 198, 220, 242, 330, 363, 396, 484, 495, 605, 660, 726, 990, 1089, 1210, 1452, 1815, 1980, 2178, 2420, 3630, 4356, 5445, 7260, 10890

Step-4: Factors of 21800

List of positive integer factors of 21800 that divides 21780 without a remainder.

1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 109, 200, 218, 436, 545, 872, 1090, 2180, 2725, 4360, 5450, 10900

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 21780 and 21800. The biggest common factor number is the GCF number.
So the greatest common factor 21780 and 21800 is 20.

Also check out the Least Common Multiple of 21780 and 21800