5328

5328 is a positive integer and part of the natural numbers. In prime factorization terms, it factors as 5328 = 2^4 × 3^2 × 37, which can be written equivalently as 16 × 333 or 144 × 37. This makes 5328 an even, composite number with multiple representations as a product of primes.

From the factorization, 5328 has 30 positive divisors, calculated as (4+1) × (2+1) × (1+1) = 5 × 3 × 2. The number is divisible by many common small integers: 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72, 144, and 37, among others. It is also divisible by 666, since 5328 = 666 × 8.

In base-10 arithmetic, the sum of the digits of 5328 is 5+3+2+8 = 18, so 5328 is divisible by 18; indeed 5328 ÷ 18 = 296. Consequently, 5328 is a Harshad (Niven) number in base 10, a property where the number is divisible by the sum of its digits. The digit sum also yields a digital root of 9, reflecting divisibility by 9 and by 3.

Beyond its role as a mathematical integer, 5328 serves as an example of a number with a compact prime factorization and a rich set of divisors, illustrating how prime decomposition governs divisibility and related numerical properties.