3688800 has 144 divisors (see below), whose sum is σ = 12655440. Its totient is φ = 931840.

The previous prime is 3688787. The next prime is 3688801. The reversal of 3688800 is 88863.

3688800 is an esthetic number in base 7, because in such base its adjacent digits differ by 1.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (3688801) by changing a digit.

It is a polite number, since it can be written in 23 ways as a sum of consecutive naturals, for example, 69574 + ... + 69626.

It is an arithmetic number, because the mean of its divisors is an integer number (87885).

Almost surely, 2^3688800 is an apocalyptic number.

3688800 is a gapful number since it is divisible by the number (30) 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 3688800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (6327720).

3688800 is an abundant number, since it is smaller than the sum of its proper divisors (8966640).

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

3688800 is a wasteful number, since it uses less digits than its factorization.

3688800 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 105 (or 92 counting only the distinct ones).

The product of its (nonzero) digits is 9216, while the sum is 33.

The square root of 3688800 is about 1920.6248983078. The cubic root of 3688800 is about 154.5118182013.

The spelling of 3688800 in words is "three million, six hundred eighty-eight thousand, eight hundred".