What is the Greatest Common Factor of 1689 and 1701?

Greatest common factor (GCF) of 1689 and 1701 is 3.

GCF(1689,1701) = 3

We will now calculate the prime factors of 1689 and 1701, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1689 and 1701.

How to find the GCF of 1689 and 1701?

We will first find the prime factorization of 1689 and 1701. After we will calculate the factors of 1689 and 1701 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 1701

Prime factors of 1701 are 3, 7. Prime factorization of 1701 in exponential form is:

1701 = 3⁵ × 7¹

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 1701

List of positive integer factors of 1701 that divides 1689 without a remainder.

1, 3, 7, 9, 21, 27, 63, 81, 189, 243, 567

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1689 and 1701. The biggest common factor number is the GCF number.
So the greatest common factor 1689 and 1701 is 3.

Also check out the Least Common Multiple of 1689 and 1701