What is the Greatest Common Factor of 13702 and 13719?

Greatest common factor (GCF) of 13702 and 13719 is 17.

GCF(13702,13719) = 17

We will now calculate the prime factors of 13702 and 13719, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 13702 and 13719.

How to find the GCF of 13702 and 13719?

We will first find the prime factorization of 13702 and 13719. After we will calculate the factors of 13702 and 13719 and find the biggest common factor number .

Step-1: Prime Factorization of 13702

Prime factors of 13702 are 2, 13, 17, 31. Prime factorization of 13702 in exponential form is:

13702 = 2¹ × 13¹ × 17¹ × 31¹

Step-2: Prime Factorization of 13719

Prime factors of 13719 are 3, 17, 269. Prime factorization of 13719 in exponential form is:

13719 = 3¹ × 17¹ × 269¹

Step-3: Factors of 13702

List of positive integer factors of 13702 that divides 13702 without a remainder.

1, 2, 13, 17, 26, 31, 34, 62, 221, 403, 442, 527, 806, 1054, 6851

Step-4: Factors of 13719

List of positive integer factors of 13719 that divides 13702 without a remainder.

1, 3, 17, 51, 269, 807, 4573

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 13702 and 13719. The biggest common factor number is the GCF number.
So the greatest common factor 13702 and 13719 is 17.

Also check out the Least Common Multiple of 13702 and 13719