What is the Greatest Common Factor of 39729 and 39748?

Greatest common factor (GCF) of 39729 and 39748 is 19.

GCF(39729,39748) = 19

We will now calculate the prime factors of 39729 and 39748, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 39729 and 39748.

How to find the GCF of 39729 and 39748?

We will first find the prime factorization of 39729 and 39748. After we will calculate the factors of 39729 and 39748 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 39748

Prime factors of 39748 are 2, 19, 523. Prime factorization of 39748 in exponential form is:

39748 = 2² × 19¹ × 523¹

Step-3: Factors of 39729

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

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

Step-4: Factors of 39748

List of positive integer factors of 39748 that divides 39729 without a remainder.

1, 2, 4, 19, 38, 76, 523, 1046, 2092, 9937, 19874

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 39729 and 39748. The biggest common factor number is the GCF number.
So the greatest common factor 39729 and 39748 is 19.

Also check out the Least Common Multiple of 39729 and 39748