What is the Greatest Common Factor of 27714 and 27729?

Greatest common factor (GCF) of 27714 and 27729 is 3.

GCF(27714,27729) = 3

We will now calculate the prime factors of 27714 and 27729, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 27714 and 27729.

How to find the GCF of 27714 and 27729?

We will first find the prime factorization of 27714 and 27729. After we will calculate the factors of 27714 and 27729 and find the biggest common factor number .

Step-1: Prime Factorization of 27714

Prime factors of 27714 are 2, 3, 31, 149. Prime factorization of 27714 in exponential form is:

27714 = 2¹ × 3¹ × 31¹ × 149¹

Step-2: Prime Factorization of 27729

Prime factors of 27729 are 3, 13, 79. Prime factorization of 27729 in exponential form is:

27729 = 3³ × 13¹ × 79¹

Step-3: Factors of 27714

List of positive integer factors of 27714 that divides 27714 without a remainder.

1, 2, 3, 6, 31, 62, 93, 149, 186, 298, 447, 894, 4619, 9238, 13857

Step-4: Factors of 27729

List of positive integer factors of 27729 that divides 27714 without a remainder.

1, 3, 9, 13, 27, 39, 79, 117, 237, 351, 711, 1027, 2133, 3081, 9243

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 27714 and 27729. The biggest common factor number is the GCF number.
So the greatest common factor 27714 and 27729 is 3.

Also check out the Least Common Multiple of 27714 and 27729