What is the Greatest Common Factor of 1677 and 1683?

Greatest common factor (GCF) of 1677 and 1683 is 3.

GCF(1677,1683) = 3

We will now calculate the prime factors of 1677 and 1683, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1677 and 1683.

How to find the GCF of 1677 and 1683?

We will first find the prime factorization of 1677 and 1683. After we will calculate the factors of 1677 and 1683 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 1683

Prime factors of 1683 are 3, 11, 17. Prime factorization of 1683 in exponential form is:

1683 = 3² × 11¹ × 17¹

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 1683

List of positive integer factors of 1683 that divides 1677 without a remainder.

1, 3, 9, 11, 17, 33, 51, 99, 153, 187, 561

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1677 and 1683. The biggest common factor number is the GCF number.
So the greatest common factor 1677 and 1683 is 3.

Also check out the Least Common Multiple of 1677 and 1683