8256

8256 is a positive integer. In decimal notation it is written as 8256. It has representations in other common bases: hexadecimal 0x2040, octal 0o20100, and binary 10000001000000.

Mathematical properties of 8256 include its prime factorization and divisors. The prime factorization is 2^6 × 3 × 43, since 8256 = 64 × 129 and 129 = 3 × 43. From this factorization the number of positive divisors is (6+1) × (1+1) × (1+1) = 28. The sum of all positive divisors is (2^7−1)/(2−1) × (3^2−1)/(3−1) × (43^2−1)/(43−1) = 127 × 4 × 44 = 22352, so the sum of proper divisors is 14096. Because this is greater than 8256, 8256 is an abundant number, with an abundance of 5840.

Divisibility and representations in practice. 8256 is divisible by 2 and by 3 (digit sum is 21), and it is divisible by powers of two up to 2^6, including 4, 8, 16, 32, and 64. It is also divisible by 43, as 8256 = 43 × 192, and by combinations of these prime factors (for example 2^a × 3^b × 43^c with a ≤ 6, b ∈ {0,1}, c ∈ {0,1}). In other bases, it equals 0x2040 in hexadecimal, 0o20100 in octal, and binary 10000001000000.

Context. As a number, 8256 is notable for its factorization and its status as an even, composite, abundant integer. It serves as an example in discussions of divisor functions, base representations, and modular arithmetic.