What is the Greatest Common Factor of 1674 and 1689?

Greatest common factor (GCF) of 1674 and 1689 is 3.

GCF(1674,1689) = 3

We will now calculate the prime factors of 1674 and 1689, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1674 and 1689.

How to find the GCF of 1674 and 1689?

We will first find the prime factorization of 1674 and 1689. After we will calculate the factors of 1674 and 1689 and find the biggest common factor number .

Step-1: Prime Factorization of 1674

Prime factors of 1674 are 2, 3, 31. Prime factorization of 1674 in exponential form is:

1674 = 2¹ × 3³ × 31¹

Step-2: Prime Factorization of 1689

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

1689 = 3¹ × 563¹

Step-3: Factors of 1674

List of positive integer factors of 1674 that divides 1674 without a remainder.

1, 2, 3, 6, 9, 18, 27, 31, 54, 62, 93, 186, 279, 558, 837

Step-4: Factors of 1689

List of positive integer factors of 1689 that divides 1674 without a remainder.

1, 3, 563

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1674 and 1689. The biggest common factor number is the GCF number.
So the greatest common factor 1674 and 1689 is 3.

Also check out the Least Common Multiple of 1674 and 1689