34320

34320 is a natural number in the sequence of integers, following 34319 and preceding 34321. It is an even number, divisible by 2. Its prime factorization is 2^4 * 3 * 5 * 71. This means that its divisors are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48, 60, 71, 80, 96, 105, 120, 142, 160, 213, 240, 284, 355, 426, 472, 568, 710, 848, 1065, 1136, 1420, 1716, 2130, 2380, 2492, 2840, 3550, 4260, 5340, 6705, 7100, 8550, 10650, 17160, and 34320.

In the realm of mathematics, 34320 appears in various contexts. For example, it is the number of ways to arrange 15 distinct items in a circle and then color each item with one of 7 colors, with rotations being considered the same but reflections distinct. It is also the value of a specific coefficient in the expansion of a particular generating function related to partitions of integers.

Beyond pure mathematics, the number 34320 might hold significance in specific fields or contexts, though without further information, its exact relevance remains unspecified. For instance, it could represent a quantity, a measurement, an identifier, or a data point in scientific research, engineering, economics, or other disciplines. Its properties as an integer, such as its divisibility and prime factors, are its most universally recognized characteristics.