8967

8967 is a natural number that follows 8966 and precedes 8968. It is an odd composite integer. Its prime factorization is 3 × 7^2 × 61, which yields twelve positive divisors. The positive divisors are 1, 3, 7, 21, 49, 61, 147, 183, 427, 1281, 2989, and 8967.

The sum of its digits is 30, so the number is divisible by 3 but not by 9. It is not a perfect power (not a square or a cube). In modular arithmetic, 8967 ≡ 3 (mod 4) and ≡ 7 (mod 8). In hexadecimal, 8967 is 0x2307, and in binary it is 10001100000111_2, which corresponds to the prime-factor-based decomposition 2^13 + 2^9 + 2^8 + 2^2 + 2^1 + 2^0.

Beyond these arithmetic properties, 8967 does not have any widely noted mathematical constants or cultural significance associated with it. It serves as an example of a small composite number with a straightforward factorization, illustrating divisor counting and basic modular behavior. As a decimal numeral, it conforms to standard base-10 representation and can be used in examples involving digit sums, divisibility tests, and base conversions.

---