4608

4608 is a positive integer known for its simple prime factorization and its role in various mathematical and computing contexts. It factors as 2^9 × 3^2, making it a composite, even number. Its divisors are all numbers of the form 2^a 3^b with 0 ≤ a ≤ 9 and 0 ≤ b ≤ 2, yielding a total of 30 divisors.

In number theory terms, 4608 is divisible by 9 and by 512, since it equals 9 × 512. The sum of its positive divisors is sigma(4608) = sigma(2^9) × sigma(3^2) = 1023 × 13 = 13299, so the sum of proper divisors is 13299 − 4608 = 8691. Because the sum of its proper divisors exceeds the number itself, 4608 is an abundant number. It is also a Harshad (Niven) number in base 10, since the sum of its digits is 4 + 6 + 0 + 8 = 18 and 4608 ÷ 18 = 256.

For representations, 4608 equals 0x1200 in hexadecimal and 1001000000000 in binary. In decimal form, 4608 bytes correspond to 4.5 kibibytes (KiB). This value is also a product of a power of two and a square (2^9 × 3^2), which guarantees that 4608 can be expressed as a sum of two squares, a consequence of the sum-of-two-squares theorem when primes congruent to 3 mod 4 appear with even exponent.