4560 has 40 divisors (see below), whose sum is σ = 14880. Its totient is φ = 1152.

The previous prime is 4549. The next prime is 4561. The reversal of 4560 is 654.

4560 is nontrivially palindromic in base 9.

4560 is a nontrivial binomial coefficient, being equal to C(96, 2).

It is a tau number, because it is divible by the number of its divisors (40).

It is a Harshad number since it is a multiple of its sum of digits (15).

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (4561) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (5) of ones.

It is a polite number, since it can be written in 7 ways as a sum of consecutive naturals, for example, 231 + ... + 249.

It is an arithmetic number, because the mean of its divisors is an integer number (372).

4560 is a gapful number since it is divisible by the number (40) formed by its first and last digit.

4560 is the 95-th triangular number and also the 48-th hexagonal number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 4560, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (7440).

4560 is an abundant number, since it is smaller than the sum of its proper divisors (10320).

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

4560 is a wasteful number, since it uses less digits than its factorization.

4560 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 35 (or 29 counting only the distinct ones).

The product of its (nonzero) digits is 120, while the sum is 15.

The square root of 4560 is about 67.5277720645. The cubic root of 4560 is about 16.5826886837.

It can be divided in two parts, 45 and 60, that added together give a triangular number (105 = T₁₄).

The spelling of 4560 in words is "four thousand, five hundred sixty".