2508000

2,508,000 is a natural number that follows 2,507,999 and precedes 2,508,001. In mathematical terms, it is an even composite number with a well-defined prime factorization and divisor structure, making it suitable for illustrating several basic number-theory concepts.

Its prime factorization is 2^5 × 3 × 5^3 × 11 × 19. From this factorization, one can derive that 2,508,000 has 192 positive divisors. The number is divisible by 1000, and because the exponent of 2 is 5 while the exponent of 5 is 3, it has exactly three trailing zeros in base 10. It is not a perfect square, since many prime exponents are odd.

Other arithmetic properties include that the sum of all positive divisors of 2,508,000 is 9,434,880, and the sum of its proper divisors (excluding the number itself) is 6,926,880, indicating that the number is abundant (the sum of proper divisors exceeds the number). The number is divisible by 125, 11, 19, and 3, as well as by 8 and 32, reflecting its composite structure and multiple small prime factors.

In contexts beyond pure number theory, 2,508,000 can appear as a large integer in calculations, data identifiers, or examples illustrating divisibility and factorization. It serves as a representative case of a highly composite, non-square, even integer with a substantial divisor set. See also: natural numbers, prime factorization, divisor function.