12944

12944 is a natural number that follows 12943 and precedes 12945. It is an even composite number with a simple prime factorization: 12944 = 2^4 × 809, where 809 is a prime number. This factorization yields a total of 10 positive divisors: 1, 2, 4, 8, 16, 809, 1618, 3236, 6472, and 12944.

As a product of a power of two and a prime congruent to 1 modulo 4, 12944 admits representations as a sum of two squares. In particular, one such representation is 12944 = 112^2 + 20^2. This aligns with Fermat’s two-square theorem, since 809 is 1 mod 4 and the factor 2^4 does not obstruct a sum-of-squares expression.

In hexadecimal notation, 12944 is 0x3290, a carryover result of converting the decimal value into base 16. The number is divisible by 16, but not by 3 or 5, as indicated by its digit sum (1 + 2 + 9 + 4 + 4 = 20) and its last digit.

Beyond its arithmetic properties, 12944 serves as an example of an even composite number with a small power-of-two factor and a larger odd prime, illustrating how such numbers can have multiple divisors and diverse representations, such as sums of squares, in a concise form.