129600

129,600 is a natural number notable for being a perfect square, equal to 360 squared. It is an even number and can be written in several compact forms that reveal its composition.

Its prime factorization is 2^6 × 3^4 × 5^2, which confirms that it is a perfect square with a square root of 360. Based on this factorization, the number of positive divisors is (6+1)(4+1)(2+1) = 105. It can also be expressed as 6^4 × 10^2 and as 360^2, illustrating its structure as a product of small primes and as a square.

In terms of representations and relationships, 129,600 can be viewed as a square of a highly composite base (360), linking it to the well-known 360 units in a circle’s degree measure. It is also the product of ordinary decimal powers: 2^6 × 3^4 × 5^2, and equals 100 × 1296, since 1296 = 6^4.

A practical numerical fact is that 129,600 seconds constitute 36 hours, i.e., 1.5 days. This highlights a simple time-related interpretation of the number outside pure arithmetic. In geometric contexts, 360^2 frequently appears in calculations involving squares or grids with a 360-unit scale, reinforcing the number’s connection to the familiar circle-based constant.

See also: square numbers, prime factorization, divisor function.