16611

16611 is a natural number that follows 16610 and precedes 16612. It is an odd, composite integer and is used in mathematical examples to illustrate factorization and related concepts.

The prime factorization of 16611 is 3 × 7^2 × 113. This shows that the number is divisible by 3, by 7, and by 113. In fact, 16611 can also be expressed as 21 × 791, underscoring its composition from smaller prime factors.

In number theory, the number of ways to express a positive integer as a sum of consecutive positive integers equals the number of odd divisors of that integer. For 16611, the exponents in its prime factorization are 1, 2, and 1, giving (1+1) × (2+1) × (1+1) = 12 odd divisors. Therefore, there are 12 representations as a sum of consecutive positive integers, including the trivial one-term representation; excluding that, there are 11 representations with two or more terms.

Other arithmetic properties include that 16611 ≡ 3 (mod 4) and that it is a multiple of 21. Its Euler totient function value is φ(16611) = 9,408, and the sum of its digits is 15, giving a digital root of 6. These features make 16611 a representative example of a mid-range composite number in introductory number theory.