4608 has 30 divisors (see below), whose sum is σ = 13299. Its totient is φ = 1536.

The previous prime is 4603. The next prime is 4621. The reversal of 4608 is 8064.

It is a powerful number, because all its prime factors have an exponent greater than 1 and also an Achilles number because it is not a perfect power.

It is a Jordan-Polya number, since it can be written as (4!)^{2} ⋅ (2!)^{3}.

It can be written as a sum of positive squares in only one way, i.e., 2304 + 2304 = 48^2 + 48^2 .

It is an ABA number since it can be written as A⋅B^{A}, here for A=9, B=2.

It is a Harshad number since it is a multiple of its sum of digits (18).

It is a nialpdrome in base 6 and base 8.

It is a zygodrome in base 8.

It is not an unprimeable number, because it can be changed into a prime (4603) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (2) of ones.

It is a polite number, since it can be written in 2 ways as a sum of consecutive naturals, for example, 1535 + 1536 + 1537.

4608 is a gapful number since it is divisible by the number (48) formed by its first and last digit.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 4608

4608 is an abundant number, since it is smaller than the sum of its proper divisors (8691).

It is a pseudoperfect number, because it is the sum of a subset of its proper divisors.

4608 is an equidigital number, since it uses as much as digits as its factorization.

4608 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 24 (or 5 counting only the distinct ones).

The product of its (nonzero) digits is 192, while the sum is 18.

The square root of 4608 is about 67.8822509939. The cubic root of 4608 is about 16.6406705844.

Multiplying 4608 by its sum of digits (18), we get a square (82944 = 288^{2}).

4608 divided by its sum of digits (18) gives a 8-th power (256 = 2^{8}).

Multiplying 4608 by its product of nonzero digits (192), we get a cube (884736 = 96^{3}).

The spelling of 4608 in words is "four thousand, six hundred eight".

Divisors: 1 2 3 4 6 8 9 12 16 18 24 32 36 48 64 72 96 128 144 192 256 288 384 512 576 768 1152 1536 2304 4608

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