7800 has 48 divisors (see below), whose sum is σ = 26040. Its totient is φ = 1920.

The previous prime is 7793. The next prime is 7817. The reversal of 7800 is 87.

7800 is nontrivially palindromic in base 14.

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

It is a nialpdrome in base 5.

It is a zygodrome in base 2 and base 5.

It is a self number, because there is not a number n which added to its sum of digits gives 7800.

It is a congruent number.

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, 594 + ... + 606.

2⁷⁸⁰⁰ 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 7800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (13020).

7800 is an abundant number, since it is smaller than the sum of its proper divisors (18240).

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

7800 is a wasteful number, since it uses less digits than its factorization.

7800 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 32 (or 23 counting only the distinct ones).

The product of its (nonzero) digits is 56, while the sum is 15.

The square root of 7800 is about 88.3176086633. The cubic root of 7800 is about 19.8319248268.

Subtracting from 7800 its product of nonzero digits (56), we obtain a square (7744 = 88²).

Adding to 7800 its reverse (87), we get a palindrome (7887).

The spelling of 7800 in words is "seven thousand, eight hundred".