86400

86400 is the number of seconds in a standard day. In conventional timekeeping, a day is defined as 24 hours, with 1 hour equal to 60 minutes and 1 minute equal to 60 seconds, giving 24 × 60 × 60 = 86,400 seconds. The prime factorization of 86400 is 2^7 × 3^3 × 5^2, and it has 96 positive divisors.

In the context of civil timekeeping, 86,400 seconds is a nominal day length. Because the Earth's rotation is irregular, the length of a day can vary slightly, and leap seconds are occasionally added to Coordinated Universal Time (UTC) to keep it aligned with mean solar time. On days when a leap second is added, the day lasts 86,401 seconds; most days remain at 86,400 seconds.

Mathematically, 86400 is an even, composite number and an abundant number, since the sum of its proper divisors (229,800) exceeds the number itself. It is also a convenient round number in computing and time calculations because it represents a full day in seconds and appears in various formulas and data representations that rely on time intervals.

In practical use, 86400 seconds per day underpins many programming libraries, time arithmetic, and calendar computations. Unix time and other systems often measure durations in seconds, with daily conversions using this standard day length, while leap seconds introduce occasional exceptions to the exact 86,400-second value in civil timekeeping.