9963

9963 is a positive integer. Its prime factorization is 3^5 × 41, which makes it a composite number. It has 12 positive divisors: 1, 3, 9, 27, 41, 81, 123, 243, 369, 1107, 3321, 9963. The factorization also shows that 9963 equals 27 × 369 and 81 × 123, among other combinations.

In base representations, 9963 can be written as 10011011101011 in binary, and as 0x26EB in hexadecimal. In base 3, it equals 111200000_3, consistent with its expression as 41 × 3^5.

The number is an odd Harshad (Niven) number in base 10, since the sum of its digits is 27 and 9963 is divisible by 27 (and hence by 9). Its divisibility by 3^5 shows a strong connection to powers of 3. Because 3 ≡ 3 (mod 4) appears with odd exponent in its prime factorization, 9963 cannot be expressed as a sum of two squares.

Miscellaneous notes include that 9963 is not a triangular or Fibonacci number, and its magnitude places it in the thousands, far from common simple constants but within typical ranges for integer factorization examples.

In summary, 9963 is a mid-sized composite number with a clear factor structure (3^5 × 41), a dozen divisors, and multiple standard base representations, illustrating several elementary number theory concepts such as Harshad numbers, sums of squares, and base conversions.