What is the Greatest Common Factor of 13702 and 13708?

Greatest common factor (GCF) of 13702 and 13708 is 2.

GCF(13702,13708) = 2

We will now calculate the prime factors of 13702 and 13708, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 13702 and 13708.

How to find the GCF of 13702 and 13708?

We will first find the prime factorization of 13702 and 13708. After we will calculate the factors of 13702 and 13708 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 13708

Prime factors of 13708 are 2, 23, 149. Prime factorization of 13708 in exponential form is:

13708 = 2² × 23¹ × 149¹

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 13708

List of positive integer factors of 13708 that divides 13702 without a remainder.

1, 2, 4, 23, 46, 92, 149, 298, 596, 3427, 6854

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 13702 and 13708. The biggest common factor number is the GCF number.
So the greatest common factor 13702 and 13708 is 2.

Also check out the Least Common Multiple of 13702 and 13708