What is the Greatest Common Factor of 1689 and 1708?

Greatest common factor (GCF) of 1689 and 1708 is 1.

GCF(1689,1708) = 1

We will now calculate the prime factors of 1689 and 1708, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1689 and 1708.

How to find the GCF of 1689 and 1708?

We will first find the prime factorization of 1689 and 1708. After we will calculate the factors of 1689 and 1708 and find the biggest common factor number .

Step-1: Prime Factorization of 1689

Prime factors of 1689 are 3, 563. Prime factorization of 1689 in exponential form is:

1689 = 3¹ × 563¹

Step-2: Prime Factorization of 1708

Prime factors of 1708 are 2, 7, 61. Prime factorization of 1708 in exponential form is:

1708 = 2² × 7¹ × 61¹

Step-3: Factors of 1689

List of positive integer factors of 1689 that divides 1689 without a remainder.

1, 3, 563

Step-4: Factors of 1708

List of positive integer factors of 1708 that divides 1689 without a remainder.

1, 2, 4, 7, 14, 28, 61, 122, 244, 427, 854

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1689 and 1708. The biggest common factor number is the GCF number.
So the greatest common factor 1689 and 1708 is 1.

Also check out the Least Common Multiple of 1689 and 1708