What is the Greatest Common Factor of 21709 and 21728?

Greatest common factor (GCF) of 21709 and 21728 is 1.

GCF(21709,21728) = 1

We will now calculate the prime factors of 21709 and 21728, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 21709 and 21728.

How to find the GCF of 21709 and 21728?

We will first find the prime factorization of 21709 and 21728. After we will calculate the factors of 21709 and 21728 and find the biggest common factor number .

Step-1: Prime Factorization of 21709

Prime factors of 21709 are 17, 1277. Prime factorization of 21709 in exponential form is:

21709 = 17¹ × 1277¹

Step-2: 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-3: Factors of 21709

List of positive integer factors of 21709 that divides 21709 without a remainder.

1, 17, 1277

Step-4: Factors of 21728

List of positive integer factors of 21728 that divides 21709 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 21709 and 21728. The biggest common factor number is the GCF number.
So the greatest common factor 21709 and 21728 is 1.

Also check out the Least Common Multiple of 21709 and 21728