3661

3661 (three thousand six hundred sixty-one) is a natural number that follows 3660 and precedes 3662. It is used in arithmetic and classification contexts as a representative integer.

Mathematical properties

3661 is composite, with prime factorization 7 × 523. Both 7 and 523 are primes, so 3661 is a semiprime. Its positive divisors are 1, 7, 523, and 3661. The sum of all divisors is 4192, making the sum of proper divisors 531. Euler’s totient function gives φ(3661) = (7−1)(523−1) = 3132.

Representations in different bases

In decimal notation it is 3661. In binary it is 111001001101, in octal 7115, and in hexadecimal E4D. In Roman numerals it can be written as MMMDCLXI.

Related number-theory notes

As a product of two primes congruent to 3 modulo 4, 3661 cannot be expressed as a sum of two squares. Its arithmetic properties also include a digital root of 7 and a value of 3661 ≡ 0 (mod 7) due to its factorization.

Context and usage

3661 appears primarily as a mathematical example and identifier within numerical catalogs. It does not have widely noted historical, astronomical, or cultural significance beyond its role as a distinct integer.