9361

9361 is a positive integer that appears in various mathematical contexts. In number theory, it is notable as a composite, square-free number with prime factorization 9361 = 11 × 23 × 37. Because the factors are distinct, its positive divisors are 1, 11, 23, 37, 253, 407, 851, and 9361.

As a result of its factorization, 9361 is an odd number and is not prime. Its Euler totient can be computed for a product of distinct primes: φ(9361) = (11−1)(23−1)(37−1) = 10 × 22 × 36 = 7920. This value counts the integers up to 9361 that are relatively prime to 9361.

Numeral representations include 9361 in base-10, 10010010010001 in binary, and 0x2491 in hexadecimal. This binary form highlights a sparse pattern, with ones at positions corresponding to the powers 2^13, 2^10, 2^7, 2^4, and 2^0.

Modular properties follow from its divisibility: 9361 ≡ 1 modulo 2, 3, 5, 8, and 9, among others. The prime factors 11, 23, and 37 are all odd, reinforcing its parity and modular behavior.

Because it factors into three small primes, 9361 commonly appears in exercises involving prime factorization, divisors, and modular arithmetic. Beyond pure mathematics, numbers like 9361 often serve as identifiers or constants in computational and educational contexts.