4563

4563 is a natural number that lies between 4562 and 4564. It is an odd composite number with prime factorization 3^3 × 13^2, making it divisible by 3, by 9, and by higher powers associated with its prime factors.

Its positive divisors are 1, 3, 9, 27, 13, 39, 117, 351, 169, 507, 1521, and 4563, for a total of 12 divisors. The sum of the proper divisors (excluding itself) is 2757, so 4563 is a deficient number (not perfect or abundant). The sum of all divisors is 7320.

In base representations, 4563 equals 1000111010011 in binary, 10723 in octal, and 11D3 in hexadecimal. Its digital root is 9, since the sum of digits is 18; therefore it is divisible by 9 and by 3, reflecting its factorization.

In mathematics, 4563 is often cited as an example of a composite number with a nontrivial factorization, illustrating how a number can be the product of repeated prime factors (a cube of 3 times a square of 13). Its properties—such as divisor count, deficient status, and multiple-base representations—can be used to demonstrate basic number-theory concepts like factorization, divisors, and base conversion. Outside pure math, 4563 may appear in catalogs, enumerations, or hypothetical date-like notations where precise numeric values are relevant.