What is the Greatest Common Factor of 21768 and 21774?

Greatest common factor (GCF) of 21768 and 21774 is 6.

GCF(21768,21774) = 6

We will now calculate the prime factors of 21768 and 21774, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 21768 and 21774.

How to find the GCF of 21768 and 21774?

We will first find the prime factorization of 21768 and 21774. After we will calculate the factors of 21768 and 21774 and find the biggest common factor number .

Step-1: Prime Factorization of 21768

Prime factors of 21768 are 2, 3, 907. Prime factorization of 21768 in exponential form is:

21768 = 2³ × 3¹ × 907¹

Step-2: 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-3: Factors of 21768

List of positive integer factors of 21768 that divides 21768 without a remainder.

1, 2, 3, 4, 6, 8, 12, 24, 907, 1814, 2721, 3628, 5442, 7256, 10884

Step-4: Factors of 21774

List of positive integer factors of 21774 that divides 21768 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 21768 and 21774. The biggest common factor number is the GCF number.
So the greatest common factor 21768 and 21774 is 6.

Also check out the Least Common Multiple of 21768 and 21774