What is the Greatest Common Factor of 21728 and 21746?

Greatest common factor (GCF) of 21728 and 21746 is 2.

GCF(21728,21746) = 2

We will now calculate the prime factors of 21728 and 21746, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 21728 and 21746.

How to find the GCF of 21728 and 21746?

We will first find the prime factorization of 21728 and 21746. After we will calculate the factors of 21728 and 21746 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 21746

Prime factors of 21746 are 2, 83, 131. Prime factorization of 21746 in exponential form is:

21746 = 2¹ × 83¹ × 131¹

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 21746

List of positive integer factors of 21746 that divides 21728 without a remainder.

1, 2, 83, 131, 166, 262, 10873

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 21728 and 21746. The biggest common factor number is the GCF number.
So the greatest common factor 21728 and 21746 is 2.

Also check out the Least Common Multiple of 21728 and 21746