What is the Greatest Common Factor of 1724 and 1728?

Greatest common factor (GCF) of 1724 and 1728 is 4.

GCF(1724,1728) = 4

We will now calculate the prime factors of 1724 and 1728, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1724 and 1728.

How to find the GCF of 1724 and 1728?

We will first find the prime factorization of 1724 and 1728. After we will calculate the factors of 1724 and 1728 and find the biggest common factor number .

Step-1: Prime Factorization of 1724

Prime factors of 1724 are 2, 431. Prime factorization of 1724 in exponential form is:

1724 = 2² × 431¹

Step-2: Prime Factorization of 1728

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

1728 = 2⁶ × 3³

Step-3: Factors of 1724

List of positive integer factors of 1724 that divides 1724 without a remainder.

1, 2, 4, 431, 862

Step-4: Factors of 1728

List of positive integer factors of 1728 that divides 1724 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1724 and 1728. The biggest common factor number is the GCF number.
So the greatest common factor 1724 and 1728 is 4.

Also check out the Least Common Multiple of 1724 and 1728