What is the Greatest Common Factor of 21774 and 21780?

Greatest common factor (GCF) of 21774 and 21780 is 6.

GCF(21774,21780) = 6

We will now calculate the prime factors of 21774 and 21780, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 21774 and 21780.

How to find the GCF of 21774 and 21780?

We will first find the prime factorization of 21774 and 21780. After we will calculate the factors of 21774 and 21780 and find the biggest common factor number .

Step-1: Prime Factorization of 21774

Prime factors of 21774 are 2, 3, 19, 191. Prime factorization of 21774 in exponential form is:

21774 = 2¹ × 3¹ × 19¹ × 191¹

Step-2: 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-3: Factors of 21774

List of positive integer factors of 21774 that divides 21774 without a remainder.

1, 2, 3, 6, 19, 38, 57, 114, 191, 382, 573, 1146, 3629, 7258, 10887

Step-4: Factors of 21780

List of positive integer factors of 21780 that divides 21774 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 21774 and 21780. The biggest common factor number is the GCF number.
So the greatest common factor 21774 and 21780 is 6.

Also check out the Least Common Multiple of 21774 and 21780