What is the Greatest Common Factor of 19665 and 19685?

Greatest common factor (GCF) of 19665 and 19685 is 5.

GCF(19665,19685) = 5

We will now calculate the prime factors of 19665 and 19685, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 19665 and 19685.

How to find the GCF of 19665 and 19685?

We will first find the prime factorization of 19665 and 19685. After we will calculate the factors of 19665 and 19685 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 19685

Prime factors of 19685 are 5, 31, 127. Prime factorization of 19685 in exponential form is:

19685 = 5¹ × 31¹ × 127¹

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 19685

List of positive integer factors of 19685 that divides 19665 without a remainder.

1, 5, 31, 127, 155, 635, 3937

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 19665 and 19685. The biggest common factor number is the GCF number.
So the greatest common factor 19665 and 19685 is 5.

Also check out the Least Common Multiple of 19665 and 19685