7688800 has 72 divisors (see below), whose sum is σ = 21467376. Its totient is φ = 2634240.

The previous prime is 7688797. The next prime is 7688809. The reversal of 7688800 is 88867.

It is a self number, because there is not a number n which added to its sum of digits gives 7688800.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (7688809) by changing a digit.

It is a polite number, since it can be written in 11 ways as a sum of consecutive naturals, for example, 4914 + ... + 6286.

It is an arithmetic number, because the mean of its divisors is an integer number (298158).

Almost surely, 2^7688800 is an apocalyptic number.

7688800 is a gapful number since it is divisible by the number (70) formed by its first and last digit.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 7688800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (10733688).

7688800 is an abundant number, since it is smaller than the sum of its proper divisors (13778576).

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

7688800 is a wasteful number, since it uses less digits than its factorization.

7688800 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 1400 (or 1387 counting only the distinct ones).

The product of its (nonzero) digits is 21504, while the sum is 37.

The square root of 7688800 is about 2772.8685507972. The cubic root of 7688800 is about 197.3722936628.

It can be divided in two parts, 7688 and 800, that multiplied together give a square (6150400 = 2480²).

The spelling of 7688800 in words is "seven million, six hundred eighty-eight thousand, eight hundred".