What is the Greatest Common Factor of 21728 and 21742?

Greatest common factor (GCF) of 21728 and 21742 is 14.

GCF(21728,21742) = 14

We will now calculate the prime factors of 21728 and 21742, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 21728 and 21742.

How to find the GCF of 21728 and 21742?

We will first find the prime factorization of 21728 and 21742. After we will calculate the factors of 21728 and 21742 and find the biggest common factor number .

Step-1: Prime Factorization of 21728

Prime factors of 21728 are 2, 7, 97. Prime factorization of 21728 in exponential form is:

21728 = 2⁵ × 7¹ × 97¹

Step-2: Prime Factorization of 21742

Prime factors of 21742 are 2, 7, 1553. Prime factorization of 21742 in exponential form is:

21742 = 2¹ × 7¹ × 1553¹

Step-3: Factors of 21728

List of positive integer factors of 21728 that divides 21728 without a remainder.

1, 2, 4, 7, 8, 14, 16, 28, 32, 56, 97, 112, 194, 224, 388, 679, 776, 1358, 1552, 2716, 3104, 5432, 10864

Step-4: Factors of 21742

List of positive integer factors of 21742 that divides 21728 without a remainder.

1, 2, 7, 14, 1553, 3106, 10871

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 21728 and 21742. The biggest common factor number is the GCF number.
So the greatest common factor 21728 and 21742 is 14.

Also check out the Least Common Multiple of 21728 and 21742