What is the Greatest Common Factor of 19665 and 19680?

Greatest common factor (GCF) of 19665 and 19680 is 15.

GCF(19665,19680) = 15

We will now calculate the prime factors of 19665 and 19680, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 19665 and 19680.

How to find the GCF of 19665 and 19680?

We will first find the prime factorization of 19665 and 19680. After we will calculate the factors of 19665 and 19680 and find the biggest common factor number .

Step-1: Prime Factorization of 19665

Prime factors of 19665 are 3, 5, 19, 23. Prime factorization of 19665 in exponential form is:

19665 = 3² × 5¹ × 19¹ × 23¹

Step-2: 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-3: Factors of 19665

List of positive integer factors of 19665 that divides 19665 without a remainder.

1, 3, 5, 9, 15, 19, 23, 45, 57, 69, 95, 115, 171, 207, 285, 345, 437, 855, 1035, 1311, 2185, 3933, 6555

Step-4: Factors of 19680

List of positive integer factors of 19680 that divides 19665 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 19665 and 19680. The biggest common factor number is the GCF number.
So the greatest common factor 19665 and 19680 is 15.

Also check out the Least Common Multiple of 19665 and 19680