40320800 has 72 divisors (see below), whose sum is σ = 106032276. Its totient is φ = 14883840.

The previous prime is 40320781. The next prime is 40320803. The reversal of 40320800 is 802304.

40320800 is digitally balanced in base 2, because in such base it contains all the possibile digits an equal number of times.

It can be written as a sum of positive squares in 6 ways, for example, as 3984016 + 36336784 = 1996^2 + 6028^2 .

It is not an unprimeable number, because it can be changed into a prime (40320803) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (13) of ones.

It is a polite number, since it can be written in 11 ways as a sum of consecutive naturals, for example, 8462 + ... + 12338.

Almost surely, 2^40320800 is an apocalyptic number.

40320800 is a gapful number since it is divisible by the number (40) 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 40320800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (53016138).

40320800 is an abundant number, since it is smaller than the sum of its proper divisors (65711476).

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

40320800 is a wasteful number, since it uses less digits than its factorization.

40320800 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 3910 (or 3897 counting only the distinct ones).

The product of its (nonzero) digits is 192, while the sum is 17.

The square root of 40320800 is about 6349.8661403214. The cubic root of 40320800 is about 342.9070231661.

The spelling of 40320800 in words is "forty million, three hundred twenty thousand, eight hundred".