What is the Greatest Common Factor of 21771 and 21777?

Greatest common factor (GCF) of 21771 and 21777 is 3.

GCF(21771,21777) = 3

We will now calculate the prime factors of 21771 and 21777, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 21771 and 21777.

How to find the GCF of 21771 and 21777?

We will first find the prime factorization of 21771 and 21777. After we will calculate the factors of 21771 and 21777 and find the biggest common factor number .

Step-1: Prime Factorization of 21771

Prime factors of 21771 are 3, 41, 59. Prime factorization of 21771 in exponential form is:

21771 = 3² × 41¹ × 59¹

Step-2: Prime Factorization of 21777

Prime factors of 21777 are 3, 7, 17, 61. Prime factorization of 21777 in exponential form is:

21777 = 3¹ × 7¹ × 17¹ × 61¹

Step-3: Factors of 21771

List of positive integer factors of 21771 that divides 21771 without a remainder.

1, 3, 9, 41, 59, 123, 177, 369, 531, 2419, 7257

Step-4: Factors of 21777

List of positive integer factors of 21777 that divides 21771 without a remainder.

1, 3, 7, 17, 21, 51, 61, 119, 183, 357, 427, 1037, 1281, 3111, 7259

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 21771 and 21777. The biggest common factor number is the GCF number.
So the greatest common factor 21771 and 21777 is 3.

Also check out the Least Common Multiple of 21771 and 21777