What is the Greatest Common Factor of 19659 and 19665?

Greatest common factor (GCF) of 19659 and 19665 is 3.

GCF(19659,19665) = 3

We will now calculate the prime factors of 19659 and 19665, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 19659 and 19665.

How to find the GCF of 19659 and 19665?

We will first find the prime factorization of 19659 and 19665. After we will calculate the factors of 19659 and 19665 and find the biggest common factor number .

Step-1: Prime Factorization of 19659

Prime factors of 19659 are 3, 6553. Prime factorization of 19659 in exponential form is:

19659 = 3¹ × 6553¹

Step-2: 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-3: Factors of 19659

List of positive integer factors of 19659 that divides 19659 without a remainder.

1, 3, 6553

Step-4: Factors of 19665

List of positive integer factors of 19665 that divides 19659 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 19659 and 19665. The biggest common factor number is the GCF number.
So the greatest common factor 19659 and 19665 is 3.

Also check out the Least Common Multiple of 19659 and 19665