14688

14688 is a five-digit integer. It falls between the integers 14687 and 14689. As an even number, it is divisible by 2. The sum of its digits is 1 + 4 + 6 + 8 + 8 = 27, which is divisible by 3 and 9. This indicates that 14688 itself is divisible by 3 and 9. Performing the division, 14688 divided by 3 equals 4896, and 14688 divided by 9 equals 1632.

In terms of prime factorization, 14688 can be broken down into its prime components. It is divisible by 2 multiple times: 14688 = 2 * 7344 = 2 * 2 * 3672 = 2 * 2 * 2 * 1836 = 2 * 2 * 2 * 2 * 918 = 2 * 2 * 2 * 2 * 2 * 459. The number 459 is divisible by 3: 459 = 3 * 153. Further factorization of 153 yields 153 = 3 * 51, and 51 = 3 * 17. Therefore, the prime factorization of 14688 is 2^5 * 3^3 * 17.

The number 14688 does not appear to have widespread significant cultural, historical, or scientific associations as a standalone entity, although specific occurrences of this number might exist within specialized datasets or contexts.