What is the Greatest Common Factor of 19686 and 19703?

Greatest common factor (GCF) of 19686 and 19703 is 17.

GCF(19686,19703) = 17

We will now calculate the prime factors of 19686 and 19703, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 19686 and 19703.

How to find the GCF of 19686 and 19703?

We will first find the prime factorization of 19686 and 19703. After we will calculate the factors of 19686 and 19703 and find the biggest common factor number .

Step-1: Prime Factorization of 19686

Prime factors of 19686 are 2, 3, 17, 193. Prime factorization of 19686 in exponential form is:

19686 = 2¹ × 3¹ × 17¹ × 193¹

Step-2: Prime Factorization of 19703

Prime factors of 19703 are 17, 19, 61. Prime factorization of 19703 in exponential form is:

19703 = 17¹ × 19¹ × 61¹

Step-3: Factors of 19686

List of positive integer factors of 19686 that divides 19686 without a remainder.

1, 2, 3, 6, 17, 34, 51, 102, 193, 386, 579, 1158, 3281, 6562, 9843

Step-4: Factors of 19703

List of positive integer factors of 19703 that divides 19686 without a remainder.

1, 17, 19, 61, 323, 1037, 1159

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 19686 and 19703. The biggest common factor number is the GCF number.
So the greatest common factor 19686 and 19703 is 17.

Also check out the Least Common Multiple of 19686 and 19703