What is the Greatest Common Factor of 27729 and 27742?

Greatest common factor (GCF) of 27729 and 27742 is 13.

GCF(27729,27742) = 13

We will now calculate the prime factors of 27729 and 27742, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 27729 and 27742.

How to find the GCF of 27729 and 27742?

We will first find the prime factorization of 27729 and 27742. After we will calculate the factors of 27729 and 27742 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 27742

Prime factors of 27742 are 2, 11, 13, 97. Prime factorization of 27742 in exponential form is:

27742 = 2¹ × 11¹ × 13¹ × 97¹

Step-3: Factors of 27729

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

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

Step-4: Factors of 27742

List of positive integer factors of 27742 that divides 27729 without a remainder.

1, 2, 11, 13, 22, 26, 97, 143, 194, 286, 1067, 1261, 2134, 2522, 13871

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 27729 and 27742. The biggest common factor number is the GCF number.
So the greatest common factor 27729 and 27742 is 13.

Also check out the Least Common Multiple of 27729 and 27742