7500 has 30 divisors (see below), whose sum is σ = 21868. Its totient is φ = 2000.

The previous prime is 7499. The next prime is 7507. The reversal of 7500 is 57.

7500 is nontrivially palindromic in base 7.

It is a tau number, because it is divible by the number of its divisors (30).

It is a Harshad number since it is a multiple of its sum of digits (12).

It is an Ulam number.

It is a nialpdrome in base 5, base 6, base 10 and base 12.

It is a zygodrome in base 5.

It is a Saint-Exupery number, since it is equal to the product of the sides of a Pythagorean triangle: 25 × 15 × 20.

It is an inconsummate number, since it does not exist a number n which divided by its sum of digits gives 7500.

It is not an unprimeable number, because it can be changed into a prime (7507) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (7) of ones.

It is a polite number, since it can be written in 9 ways as a sum of consecutive naturals, for example, 1498 + ... + 1502.

2⁷⁵⁰⁰ 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 7500, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (10934).

7500 is an abundant number, since it is smaller than the sum of its proper divisors (14368).

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

7500 is a wasteful number, since it uses less digits than its factorization.

7500 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 27 (or 10 counting only the distinct ones).

The product of its (nonzero) digits is 35, while the sum is 12.

The square root of 7500 is about 86.6025403784. The cubic root of 7500 is about 19.5743382058.

Multiplying 7500 by its sum of digits (12), we get a square (90000 = 300²).

7500 divided by its sum of digits (12) gives a 4-th power (625 = 5⁴).

Adding to 7500 its reverse (57), we get a palindrome (7557).

The spelling of 7500 in words is "seven thousand, five hundred".