7686

7686 is a natural number that follows 7685 and precedes 7687. It is an even composite integer with a prime factorization of 2 × 3^2 × 7 × 61, indicating it has 24 positive divisors. It is not a prime, nor a perfect power or a perfect square; its square root is approximately 87.7.

In terms of divisibility and modular arithmetic, the digit sum is 7 + 6 + 8 + 6 = 27, so 7686 is divisible by 3 and by 9. By its prime factorization, it is also divisible by 7 and by 61. The combination of these factors means the number has multiple distinct prime factors.

In base representations, 7686 equals 1111000000110 in binary and 0x1E06 in hexadecimal. These representations reflect its factor structure and aid in various computational tasks.

As a four-digit integer, 7686 is sometimes used as an example in arithmetic and number theory to illustrate factorization, divisor counting, and base conversions. Beyond these mathematical properties, there are no widely recognized historical events, identifiers, or common names directly associated with the number itself.