What is the Greatest Common Factor of 1728 and 1740?

Greatest common factor (GCF) of 1728 and 1740 is 12.

GCF(1728,1740) = 12

We will now calculate the prime factors of 1728 and 1740, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1728 and 1740.

How to find the GCF of 1728 and 1740?

We will first find the prime factorization of 1728 and 1740. After we will calculate the factors of 1728 and 1740 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 1740

Prime factors of 1740 are 2, 3, 5, 29. Prime factorization of 1740 in exponential form is:

1740 = 2² × 3¹ × 5¹ × 29¹

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 1740

List of positive integer factors of 1740 that divides 1728 without a remainder.

1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 29, 30, 58, 60, 87, 116, 145, 174, 290, 348, 435, 580, 870

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1728 and 1740. The biggest common factor number is the GCF number.
So the greatest common factor 1728 and 1740 is 12.

Also check out the Least Common Multiple of 1728 and 1740