19800

19800 is a natural number that follows 19799 and precedes 19801. It is an even and composite number with several notable divisibility properties and a straightforward prime factorization.

The prime factorization of 19800 is 2^3 × 3^2 × 5^2 × 11. From this factorization, the total number of positive divisors is (3+1) × (2+1) × (2+1) × (1+1) = 72. The number is divisible by 100, as well as by 9, 11, 8, 25, and many of their combinations (for example, 110, 198, 300, and 9900 are divisors). It is also a Harshad number in base 10, since the sum of its digits is 18 and 19800 ÷ 18 = 1100.

In time units, 19800 seconds equal 5 hours and 30 minutes, since 3600 seconds constitute an hour. This makes 19800 a convenient example for illustrating unit conversions between seconds and hours.

Geometrically or in combinatorics, 19800 does not have a standard widely recognized interpretation beyond its factorization and divisor structure, but it serves as a representative example of an even, highly composite integer with a clear prime decomposition and multiple practical divisors.

Overall, 19800 is notable primarily for its arithmetic properties: its factorization, divisor count, and status as a Harshad number, rather than for any particular real-world object or event associated with the exact value.