432

432 is the natural number that follows 431 and precedes 433. In mathematics it is often noted for its prime factorization, 432 = 2^4 × 3^3, and for having 20 positive divisors. It is an even, abundant number (its proper divisors sum to more than 432), with a sum-of-divisors value of 1240. The digital root is 9, and since 432 is divisible by 9, it is also a Harshad (Niven) number. In binary it is represented as 110110000.

In arithmetic and geometry, 432 appears as a product of powers of small primes, which makes it convenient in problems involving factorization, divisibility, and counting. It is divisible by 16 and by 27, and thus by many smaller integers such as 2, 3, 4, 6, 8, and 9. The number also has a straightforward decimal property: the sum of its digits is 9, reinforcing its divisibility by 9.

In timekeeping and measurement, 432 seconds equal 7 minutes and 12 seconds. There are 43,200 seconds in half a day (12 hours), which is 432 × 100, a figure sometimes cited in discussions of time-scale crystallization or daylight calculations.

In music and acoustics, 432 Hz tuning refers to a proposed alternative standard where A above middle C is set to 432 Hz rather than the modern 440 Hz. Advocates claim various harmonical, historical, or natural benefits, but the prevailing international standard remains A = 440 Hz, and evidence for the advantages of 432 Hz is primarily subjective.

Overall, 432 is a well-known composite number with several simple, well-defined properties and a modest cultural presence in discussions of tuning.