What is the Greatest Common Factor of 21744 and 21753?

Greatest common factor (GCF) of 21744 and 21753 is 9.

GCF(21744,21753) = 9

We will now calculate the prime factors of 21744 and 21753, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 21744 and 21753.

How to find the GCF of 21744 and 21753?

We will first find the prime factorization of 21744 and 21753. After we will calculate the factors of 21744 and 21753 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 21753

Prime factors of 21753 are 3, 2417. Prime factorization of 21753 in exponential form is:

21753 = 3² × 2417¹

Step-3: Factors of 21744

List of positive integer factors of 21744 that divides 21744 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

Step-4: Factors of 21753

List of positive integer factors of 21753 that divides 21744 without a remainder.

1, 3, 9, 2417, 7251

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 21744 and 21753. The biggest common factor number is the GCF number.
So the greatest common factor 21744 and 21753 is 9.

Also check out the Least Common Multiple of 21744 and 21753