7540 has 24 divisors (see below), whose sum is σ = 17640. Its totient is φ = 2688.

The previous prime is 7537. The next prime is 7541. The reversal of 7540 is 457.

7540 = 15² + 16² + ... + 29².

7540 is nontrivially palindromic in base 12.

It can be written as a sum of positive squares in 4 ways, for example, as 144 + 7396 = 12^2 + 86^2 .

7540 is a nontrivial repdigit in base 12.

It is a plaindrome in base 12 and base 15.

It is a nialpdrome in base 10 and base 12.

It is a zygodrome in base 12.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (7541) 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, 246 + ... + 274.

It is an arithmetic number, because the mean of its divisors is an integer number (735).

2⁷⁵⁴⁰ 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 7540, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (8820).

7540 is an abundant number, since it is smaller than the sum of its proper divisors (10100).

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

7540 is a wasteful number, since it uses less digits than its factorization.

7540 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 51 (or 49 counting only the distinct ones).

The product of its (nonzero) digits is 140, while the sum is 16.

The square root of 7540 is about 86.8331733844. The cubic root of 7540 is about 19.6090753474.

Adding to 7540 its reverse (457), we get a palindrome (7997).

The spelling of 7540 in words is "seven thousand, five hundred forty".