What is the Greatest Common Factor of 19680 and 19689?

Greatest common factor (GCF) of 19680 and 19689 is 3.

GCF(19680,19689) = 3

We will now calculate the prime factors of 19680 and 19689, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 19680 and 19689.

How to find the GCF of 19680 and 19689?

We will first find the prime factorization of 19680 and 19689. After we will calculate the factors of 19680 and 19689 and find the biggest common factor number .

Step-1: Prime Factorization of 19680

Prime factors of 19680 are 2, 3, 5, 41. Prime factorization of 19680 in exponential form is:

19680 = 2⁵ × 3¹ × 5¹ × 41¹

Step-2: Prime Factorization of 19689

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

19689 = 3¹ × 6563¹

Step-3: Factors of 19680

List of positive integer factors of 19680 that divides 19680 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40, 41, 48, 60, 80, 82, 96, 120, 123, 160, 164, 205, 240, 246, 328, 410, 480, 492, 615, 656, 820, 984, 1230, 1312, 1640, 1968, 2460, 3280, 3936, 4920, 6560, 9840

Step-4: Factors of 19689

List of positive integer factors of 19689 that divides 19680 without a remainder.

1, 3, 6563

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 19680 and 19689. The biggest common factor number is the GCF number.
So the greatest common factor 19680 and 19689 is 3.

Also check out the Least Common Multiple of 19680 and 19689