What is the Greatest Common Factor of 19708 and 19721?

Greatest common factor (GCF) of 19708 and 19721 is 13.

GCF(19708,19721) = 13

We will now calculate the prime factors of 19708 and 19721, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 19708 and 19721.

How to find the GCF of 19708 and 19721?

We will first find the prime factorization of 19708 and 19721. After we will calculate the factors of 19708 and 19721 and find the biggest common factor number .

Step-1: Prime Factorization of 19708

Prime factors of 19708 are 2, 13, 379. Prime factorization of 19708 in exponential form is:

19708 = 2² × 13¹ × 379¹

Step-2: Prime Factorization of 19721

Prime factors of 19721 are 13, 37, 41. Prime factorization of 19721 in exponential form is:

19721 = 13¹ × 37¹ × 41¹

Step-3: Factors of 19708

List of positive integer factors of 19708 that divides 19708 without a remainder.

1, 2, 4, 13, 26, 52, 379, 758, 1516, 4927, 9854

Step-4: Factors of 19721

List of positive integer factors of 19721 that divides 19708 without a remainder.

1, 13, 37, 41, 481, 533, 1517

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 19708 and 19721. The biggest common factor number is the GCF number.
So the greatest common factor 19708 and 19721 is 13.

Also check out the Least Common Multiple of 19708 and 19721