What is the Greatest Common Factor of 682 and 688?

Greatest common factor (GCF) of 682 and 688 is 2.

GCF(682,688) = 2

We will now calculate the prime factors of 682 and 688, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 682 and 688.

How to find the GCF of 682 and 688?

We will first find the prime factorization of 682 and 688. After we will calculate the factors of 682 and 688 and find the biggest common factor number .

Step-1: Prime Factorization of 682

Prime factors of 682 are 2, 11, 31. Prime factorization of 682 in exponential form is:

682 = 2¹ × 11¹ × 31¹

Step-2: Prime Factorization of 688

Prime factors of 688 are 2, 43. Prime factorization of 688 in exponential form is:

688 = 2⁴ × 43¹

Step-3: Factors of 682

List of positive integer factors of 682 that divides 682 without a remainder.

1, 2, 11, 22, 31, 62, 341

Step-4: Factors of 688

List of positive integer factors of 688 that divides 682 without a remainder.

1, 2, 4, 8, 16, 43, 86, 172, 344

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 682 and 688. The biggest common factor number is the GCF number.
So the greatest common factor 682 and 688 is 2.

Also check out the Least Common Multiple of 682 and 688