8415

8415 is a natural number that comes after 8414 and before 8416. It is an odd, composite number with several notable arithmetic properties.

Its prime factorization is 8415 = 3^2 × 5 × 11 × 17. This makes the number divisible by 3, 5, 9, 11, 15, and 17, among others, and explains its digit sum of 18 (which confirms divisibility by 3 and 9).

8415 has 24 positive divisors. The sum of all divisors, including itself, is 16848, so the sum of proper divisors is 16848 − 8415 = 8433. Because 8433 is greater than 8415, 8415 is classified as an abundant number, with an abundance of 8433 − 8415 = 18. The Euler totient value is φ(8415) = 3840, reflecting the count of integers up to 8415 that are relatively prime to it.

As a number in modular arithmetic, 8415 is congruent to 0 modulo 3, modulo 5, and modulo 15, due to its factorization. Its factorization into small primes also shows its structure as a product of repeated and distinct small primes.

In summary, 8415 is an odd composite with a rich factorization (3^2 × 5 × 11 × 17), a divisor count of 24, a divisor sum of 16848 (proper sum 8433), and it is an abundant number with totient 3840. It serves as a representative example of a moderately large, highly factorable integer in number-theory contexts.