7791

7791 is a natural number that sits between 7790 and 7792. In arithmetic terms it is an odd composite number with the prime factorization 7791 = 3 × 7² × 53, which means it has multiple divisors. Its positive divisors are 1, 3, 7, 21, 49, 147, 53, 159, 371, 1113, 2597, and 7791.

In standard base 10 notation it is written as 7791. Its representations in other bases include hexadecimal, where 7791 equals 1E6F, and binary, where it is 0001111001101111 (in a 16‑bit form). The number is congruent to 3 modulo 4, since 7791 mod 4 = 3, reflecting its divisibility by primes of the form 4k+3 with odd exponents.

7791 also has specific sum-of-squares properties. Because its factorization contains 3 (a prime congruent to 3 modulo 4) to the first power, 7791 cannot be expressed as a sum of two squares. Additionally, since 7791 can be written as 8b + 7 (specifically 8 × 973 + 7), Legendre’s three-square theorem implies that it cannot be expressed as the sum of three squares either.

These basic characteristics—factorization, divisors, and base representations—illustrate typical ways in which a specific natural number like 7791 is analyzed in number theory.