What is the Greatest Common Factor of 21681 and 21696?

Greatest common factor (GCF) of 21681 and 21696 is 3.

GCF(21681,21696) = 3

We will now calculate the prime factors of 21681 and 21696, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 21681 and 21696.

How to find the GCF of 21681 and 21696?

We will first find the prime factorization of 21681 and 21696. After we will calculate the factors of 21681 and 21696 and find the biggest common factor number .

Step-1: Prime Factorization of 21681

Prime factors of 21681 are 3, 11, 73. Prime factorization of 21681 in exponential form is:

21681 = 3³ × 11¹ × 73¹

Step-2: Prime Factorization of 21696

Prime factors of 21696 are 2, 3, 113. Prime factorization of 21696 in exponential form is:

21696 = 2⁶ × 3¹ × 113¹

Step-3: Factors of 21681

List of positive integer factors of 21681 that divides 21681 without a remainder.

1, 3, 9, 11, 27, 33, 73, 99, 219, 297, 657, 803, 1971, 2409, 7227

Step-4: Factors of 21696

List of positive integer factors of 21696 that divides 21681 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 113, 192, 226, 339, 452, 678, 904, 1356, 1808, 2712, 3616, 5424, 7232, 10848

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 21681 and 21696. The biggest common factor number is the GCF number.
So the greatest common factor 21681 and 21696 is 3.

Also check out the Least Common Multiple of 21681 and 21696