36768800 has 144 divisors (see below), whose sum is σ = 98431200. Its totient is φ = 13363200.

The previous prime is 36768791. The next prime is 36768829. The reversal of 36768800 is 886763.

It is a Harshad number since it is a multiple of its sum of digits (38).

It is an unprimeable number.

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 23 ways as a sum of consecutive naturals, for example, 623171 + ... + 623229.

It is an arithmetic number, because the mean of its divisors is an integer number (683550).

Almost surely, 2^36768800 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 36768800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (49215600).

36768800 is an abundant number, since it is smaller than the sum of its proper divisors (61662400).

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

36768800 is a wasteful number, since it uses less digits than its factorization.

36768800 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 139 (or 126 counting only the distinct ones).

The product of its (nonzero) digits is 48384, while the sum is 38.

The square root of 36768800 is about 6063.7282260998. The cubic root of 36768800 is about 332.5266716879.

The spelling of 36768800 in words is "thirty-six million, seven hundred sixty-eight thousand, eight hundred".