8463

8463 is a natural number that comes after 8462 and before 8464. It is an odd composite number with several notable arithmetic properties.

Its prime factorization is 3 × 7 × 13 × 31, making 8463 square-free and the product of four distinct primes. Consequently, it has 16 divisors in total. The sum of all divisors is (1+3)(1+7)(1+13)(1+31) = 4×8×14×32 = 14336, so the sum of its proper divisors is 14336 − 8463 = 5873. The Euler totient function yields φ(8463) = 8463 × (1 − 1/3) × (1 − 1/7) × (1 − 1/13) × (1 − 1/31) = 4320.

In base 10, 8463 is a Harshad (or Niven) number because it is divisible by the sum of its digits: 8 + 4 + 6 + 3 = 21 and 8463 ÷ 21 = 403. The digits 403 factor further as 13 × 31, which are two of its prime factors.

Representations of 8463 include its decimal form 8463, its hexadecimal form 0x210F, and its binary form 10000100001111. Notably, in hexadecimal, 8463 equals 2×4096 plus 1×256 plus 0×16 plus 15, totaling 0x210F.