What is the Greatest Common Factor of 27712 and 27729?

Greatest common factor (GCF) of 27712 and 27729 is 1.

GCF(27712,27729) = 1

We will now calculate the prime factors of 27712 and 27729, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 27712 and 27729.

How to find the GCF of 27712 and 27729?

We will first find the prime factorization of 27712 and 27729. After we will calculate the factors of 27712 and 27729 and find the biggest common factor number .

Step-1: Prime Factorization of 27712

Prime factors of 27712 are 2, 433. Prime factorization of 27712 in exponential form is:

27712 = 2⁶ × 433¹

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 27712

List of positive integer factors of 27712 that divides 27712 without a remainder.

1, 2, 4, 8, 16, 32, 64, 433, 866, 1732, 3464, 6928, 13856

Step-4: Factors of 27729

List of positive integer factors of 27729 that divides 27712 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 27712 and 27729. The biggest common factor number is the GCF number.
So the greatest common factor 27712 and 27729 is 1.

Also check out the Least Common Multiple of 27712 and 27729