18000

18000 is a natural number that follows 17999 and precedes 18001. It is even and composite, and it can be expressed as 18,000 in decimal notation.

Prime factorization and divisors: 18000 = 2^4 × 3^2 × 5^3. From this factorization, the number of divisors is (4+1)(2+1)(3+1) = 60. The sum of all divisors is (2^5−1)/(2−1) × (3^3−1)/(3−1) × (5^4−1)/(5−1) = 31 × 13 × 156 = 62,868, so the sum of proper divisors is 62,868 − 18,000 = 44,868. Thus 18000 is an abundant number, as the sum of its proper divisors exceeds the number itself.

Other properties: 18000 = 144 × 125, so it is divisible by 16, 9, and 125. In particular, it is divisible by 9 (and by 3) because the digit sum is 1+8+0+0+0 = 9. Its decimal form ends with three zeros, reflecting that it is a multiple of 1000.

Applications and observations: In time units, 18,000 seconds equal five hours, illustrating a convenient relation between the number and common time measurements. As a mathematical object, 18000 has a straightforward prime factorization and multiple divisors, making it useful in example problems involving divisors, multiples, and sum-of-divisors calculations.