What is the Greatest Common Factor of 21729 and 21744?

Greatest common factor (GCF) of 21729 and 21744 is 3.

GCF(21729,21744) = 3

We will now calculate the prime factors of 21729 and 21744, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 21729 and 21744.

How to find the GCF of 21729 and 21744?

We will first find the prime factorization of 21729 and 21744. After we will calculate the factors of 21729 and 21744 and find the biggest common factor number .

Step-1: Prime Factorization of 21729

Prime factors of 21729 are 3, 7243. Prime factorization of 21729 in exponential form is:

21729 = 3¹ × 7243¹

Step-2: Prime Factorization of 21744

Prime factors of 21744 are 2, 3, 151. Prime factorization of 21744 in exponential form is:

21744 = 2⁴ × 3² × 151¹

Step-3: Factors of 21729

List of positive integer factors of 21729 that divides 21729 without a remainder.

1, 3, 7243

Step-4: Factors of 21744

List of positive integer factors of 21744 that divides 21729 without a remainder.

1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144, 151, 302, 453, 604, 906, 1208, 1359, 1812, 2416, 2718, 3624, 5436, 7248, 10872

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 21729 and 21744. The biggest common factor number is the GCF number.
So the greatest common factor 21729 and 21744 is 3.

Also check out the Least Common Multiple of 21729 and 21744