What is the Greatest Common Factor of 10682 and 10689?

Greatest common factor (GCF) of 10682 and 10689 is 7.

GCF(10682,10689) = 7

We will now calculate the prime factors of 10682 and 10689, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 10682 and 10689.

How to find the GCF of 10682 and 10689?

We will first find the prime factorization of 10682 and 10689. After we will calculate the factors of 10682 and 10689 and find the biggest common factor number .

Step-1: Prime Factorization of 10682

Prime factors of 10682 are 2, 7, 109. Prime factorization of 10682 in exponential form is:

10682 = 2¹ × 7² × 109¹

Step-2: Prime Factorization of 10689

Prime factors of 10689 are 3, 7, 509. Prime factorization of 10689 in exponential form is:

10689 = 3¹ × 7¹ × 509¹

Step-3: Factors of 10682

List of positive integer factors of 10682 that divides 10682 without a remainder.

1, 2, 7, 14, 49, 98, 109, 218, 763, 1526, 5341

Step-4: Factors of 10689

List of positive integer factors of 10689 that divides 10682 without a remainder.

1, 3, 7, 21, 509, 1527, 3563

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 10682 and 10689. The biggest common factor number is the GCF number.
So the greatest common factor 10682 and 10689 is 7.

Also check out the Least Common Multiple of 10682 and 10689