What is the Greatest Common Factor of 1728 and 1746?

Greatest common factor (GCF) of 1728 and 1746 is 18.

GCF(1728,1746) = 18

We will now calculate the prime factors of 1728 and 1746, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1728 and 1746.

How to find the GCF of 1728 and 1746?

We will first find the prime factorization of 1728 and 1746. After we will calculate the factors of 1728 and 1746 and find the biggest common factor number .

Step-1: Prime Factorization of 1728

Prime factors of 1728 are 2, 3. Prime factorization of 1728 in exponential form is:

1728 = 2⁶ × 3³

Step-2: Prime Factorization of 1746

Prime factors of 1746 are 2, 3, 97. Prime factorization of 1746 in exponential form is:

1746 = 2¹ × 3² × 97¹

Step-3: Factors of 1728

List of positive integer factors of 1728 that divides 1728 without a remainder.

1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 48, 54, 64, 72, 96, 108, 144, 192, 216, 288, 432, 576, 864

Step-4: Factors of 1746

List of positive integer factors of 1746 that divides 1728 without a remainder.

1, 2, 3, 6, 9, 18, 97, 194, 291, 582, 873

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1728 and 1746. The biggest common factor number is the GCF number.
So the greatest common factor 1728 and 1746 is 18.

Also check out the Least Common Multiple of 1728 and 1746