What is the Greatest Common Factor of 39714 and 39729?

Greatest common factor (GCF) of 39714 and 39729 is 3.

GCF(39714,39729) = 3

We will now calculate the prime factors of 39714 and 39729, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 39714 and 39729.

How to find the GCF of 39714 and 39729?

We will first find the prime factorization of 39714 and 39729. After we will calculate the factors of 39714 and 39729 and find the biggest common factor number .

Step-1: Prime Factorization of 39714

Prime factors of 39714 are 2, 3, 6619. Prime factorization of 39714 in exponential form is:

39714 = 2¹ × 3¹ × 6619¹

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 39714

List of positive integer factors of 39714 that divides 39714 without a remainder.

1, 2, 3, 6, 6619, 13238, 19857

Step-4: Factors of 39729

List of positive integer factors of 39729 that divides 39714 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 39714 and 39729. The biggest common factor number is the GCF number.
So the greatest common factor 39714 and 39729 is 3.

Also check out the Least Common Multiple of 39714 and 39729