What is the Greatest Common Factor of 39723 and 39729?

Greatest common factor (GCF) of 39723 and 39729 is 3.

GCF(39723,39729) = 3

We will now calculate the prime factors of 39723 and 39729, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 39723 and 39729.

How to find the GCF of 39723 and 39729?

We will first find the prime factorization of 39723 and 39729. After we will calculate the factors of 39723 and 39729 and find the biggest common factor number .

Step-1: Prime Factorization of 39723

Prime factors of 39723 are 3, 13241. Prime factorization of 39723 in exponential form is:

39723 = 3¹ × 13241¹

Step-2: Prime Factorization of 39729

Prime factors of 39729 are 3, 17, 19, 41. Prime factorization of 39729 in exponential form is:

39729 = 3¹ × 17¹ × 19¹ × 41¹

Step-3: Factors of 39723

List of positive integer factors of 39723 that divides 39723 without a remainder.

1, 3, 13241

Step-4: Factors of 39729

List of positive integer factors of 39729 that divides 39723 without a remainder.

1, 3, 17, 19, 41, 51, 57, 123, 323, 697, 779, 969, 2091, 2337, 13243

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 39723 and 39729. The biggest common factor number is the GCF number.
So the greatest common factor 39723 and 39729 is 3.

Also check out the Least Common Multiple of 39723 and 39729