3846

3846 is a natural number that follows 3845 and precedes 3847. It is an even, composite number with prime factorization 2 × 3 × 641. Consequently, its divisors are 1, 2, 3, 6, 641, 1282, 1923, and 3846. The sum of its digits is 21, indicating divisibility by 3 and 9 is not possible, while it is divisible by 2.

In common numeral systems, 3846 is represented as follows: binary 111100000110, octal 7406, and hexadecimal F06. In Roman numerals, it is written as MMMDCCCXLVI.

A notable mathematical property is that 641, a prime factor of 3846, is historically significant because it is a divisor of Fermat number F5 (2^(2^5) + 1 = 4294967297). Specifically, 641 × 6700417 = 4294967297, which helped establish that F5 is composite. This connection is often cited in discussions of early 20th-century number theory and Fermat numbers.

Overall, 3846 is primarily recognized for its factorization and its representations across bases, as well as its incidental link to the historical study of Fermat numbers.