5040 has 60 divisors (see below), whose sum is σ = 19344. Its totient is φ = 1152.

The previous prime is 5039. The next prime is 5051. The reversal of 5040 is 405.

It is a factorial (5040 = 7 ! = 1 ⋅ 2 ⋅ 3 ⋅ 4 ⋅ 5 ⋅ 6 ⋅ 7 ), and thus also a Jordan-Polya number.

It is a Cunningham number, because it is equal to 71²-1.

It is a tau number, because it is divible by the number of its divisors (60).

It is a Harshad number since it is a multiple of its sum of digits (9).

It is a super Niven number, because it is divisible the sum of any subset of its (nonzero) digits.

It is an unprimeable number.

It is a polite number, since it can be written in 11 ways as a sum of consecutive naturals, for example, 717 + ... + 723.

5040 is a highly composite number, because it has more divisors than any smaller number.

5040 is a superabundant number, because it has a larger abundancy index than any smaller number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 5040, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (9672).

5040 is an abundant number, since it is smaller than the sum of its proper divisors (14304).

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

5040 is a wasteful number, since it uses less digits than its factorization.

5040 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 26 (or 17 counting only the distinct ones).

The product of its (nonzero) digits is 20, while the sum is 9.

The square root of 5040 is about 70.9929573972. The cubic root of 5040 is about 17.1452377646.

5040 divided by its product of nonzero digits (20) gives a palindrome (252).

Adding to 5040 its reverse (405), we get a palindrome (5445).

The spelling of 5040 in words is "five thousand, forty".