What is the Greatest Common Factor of 21726 and 21744?

Greatest common factor (GCF) of 21726 and 21744 is 18.

GCF(21726,21744) = 18

We will now calculate the prime factors of 21726 and 21744, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 21726 and 21744.

How to find the GCF of 21726 and 21744?

We will first find the prime factorization of 21726 and 21744. After we will calculate the factors of 21726 and 21744 and find the biggest common factor number .

Step-1: Prime Factorization of 21726

Prime factors of 21726 are 2, 3, 17, 71. Prime factorization of 21726 in exponential form is:

21726 = 2¹ × 3² × 17¹ × 71¹

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 21726

List of positive integer factors of 21726 that divides 21726 without a remainder.

1, 2, 3, 6, 9, 17, 18, 34, 51, 71, 102, 142, 153, 213, 306, 426, 639, 1207, 1278, 2414, 3621, 7242, 10863

Step-4: Factors of 21744

List of positive integer factors of 21744 that divides 21726 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 21726 and 21744. The biggest common factor number is the GCF number.
So the greatest common factor 21726 and 21744 is 18.

Also check out the Least Common Multiple of 21726 and 21744