5140 has 12 divisors (see below), whose sum is σ = 10836. Its totient is φ = 2048.

The previous prime is 5119. The next prime is 5147. The reversal of 5140 is 415.

5140 = 11² + 12² + ... + 25².

It can be written as a sum of positive squares in 2 ways, for example, as 3844 + 1296 = 62^2 + 36^2 .

It is a Harshad number since it is a multiple of its sum of digits (10).

5140 is an undulating number in base 16.

It is a plaindrome in base 13.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (5147) by changing a digit.

In principle, a polygon with 5140 sides can be constructed with ruler and compass.

It is a polite number, since it can be written in 3 ways as a sum of consecutive naturals, for example, 109 + ... + 148.

It is an arithmetic number, because the mean of its divisors is an integer number (903).

2⁵¹⁴⁰ is an apocalyptic number.

It is an amenable number.

5140 is an abundant number, since it is smaller than the sum of its proper divisors (5696).

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

It is a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (5418).

5140 is a wasteful number, since it uses less digits than its factorization.

5140 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 266 (or 264 counting only the distinct ones).

The product of its (nonzero) digits is 20, while the sum is 10.

The square root of 5140 is about 71.6937933157. The cubic root of 5140 is about 17.2578903901.

Adding to 5140 its reverse (415), we get a palindrome (5555).

It can be divided in two parts, 51 and 40, that added together give a triangular number (91 = T₁₃).

The spelling of 5140 in words is "five thousand, one hundred forty".