5640 has 32 divisors (see below), whose sum is σ = 17280. Its totient is φ = 1472.

The previous prime is 5639. The next prime is 5641. The reversal of 5640 is 465.

Added to its reverse (465) it gives a triangular number (6105 = T₁₁₀).

5640 is an esthetic number in base 9, because in such base its adjacent digits differ by 1.

It is an interprime number because it is at equal distance from previous prime (5639) and next prime (5641).

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

It is a nialpdrome in base 12.

It is an inconsummate number, since it does not exist a number n which divided by its sum of digits gives 5640.

It is not an unprimeable number, because it can be changed into a prime (5641) by changing a digit.

It is a polite number, since it can be written in 7 ways as a sum of consecutive naturals, for example, 97 + ... + 143.

It is an arithmetic number, because the mean of its divisors is an integer number (540).

2⁵⁶⁴⁰ is an apocalyptic number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 5640, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (8640).

5640 is an abundant number, since it is smaller than the sum of its proper divisors (11640).

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

5640 is a wasteful number, since it uses less digits than its factorization.

5640 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 61 (or 57 counting only the distinct ones).

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

The square root of 5640 is about 75.0999334221. The cubic root of 5640 is about 17.8002609060.

Subtracting from 5640 its sum of digits (15), we obtain a square (5625 = 75²).

Adding to 5640 its reverse (465), we get a triangular number (6105 = T₁₁₀).

The spelling of 5640 in words is "five thousand, six hundred forty".