What is the Greatest Common Factor of 19689 and 19704?

Greatest common factor (GCF) of 19689 and 19704 is 3.

GCF(19689,19704) = 3

We will now calculate the prime factors of 19689 and 19704, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 19689 and 19704.

How to find the GCF of 19689 and 19704?

We will first find the prime factorization of 19689 and 19704. After we will calculate the factors of 19689 and 19704 and find the biggest common factor number .

Step-1: Prime Factorization of 19689

Prime factors of 19689 are 3, 6563. Prime factorization of 19689 in exponential form is:

19689 = 3¹ × 6563¹

Step-2: Prime Factorization of 19704

Prime factors of 19704 are 2, 3, 821. Prime factorization of 19704 in exponential form is:

19704 = 2³ × 3¹ × 821¹

Step-3: Factors of 19689

List of positive integer factors of 19689 that divides 19689 without a remainder.

1, 3, 6563

Step-4: Factors of 19704

List of positive integer factors of 19704 that divides 19689 without a remainder.

1, 2, 3, 4, 6, 8, 12, 24, 821, 1642, 2463, 3284, 4926, 6568, 9852

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 19689 and 19704. The biggest common factor number is the GCF number.
So the greatest common factor 19689 and 19704 is 3.

Also check out the Least Common Multiple of 19689 and 19704