What is the Greatest Common Factor of 1677 and 1686?

Greatest common factor (GCF) of 1677 and 1686 is 3.

GCF(1677,1686) = 3

We will now calculate the prime factors of 1677 and 1686, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1677 and 1686.

How to find the GCF of 1677 and 1686?

We will first find the prime factorization of 1677 and 1686. After we will calculate the factors of 1677 and 1686 and find the biggest common factor number .

Step-1: Prime Factorization of 1677

Prime factors of 1677 are 3, 13, 43. Prime factorization of 1677 in exponential form is:

1677 = 3¹ × 13¹ × 43¹

Step-2: Prime Factorization of 1686

Prime factors of 1686 are 2, 3, 281. Prime factorization of 1686 in exponential form is:

1686 = 2¹ × 3¹ × 281¹

Step-3: Factors of 1677

List of positive integer factors of 1677 that divides 1677 without a remainder.

1, 3, 13, 39, 43, 129, 559

Step-4: Factors of 1686

List of positive integer factors of 1686 that divides 1677 without a remainder.

1, 2, 3, 6, 281, 562, 843

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1677 and 1686. The biggest common factor number is the GCF number.
So the greatest common factor 1677 and 1686 is 3.

Also check out the Least Common Multiple of 1677 and 1686