76138800 has 120 divisors (see below), whose sum is σ = 247799616. Its totient is φ = 19979520.

The previous prime is 76138771. The next prime is 76138817. The reversal of 76138800 is 883167.

It is a tau number, because it is divible by the number of its divisors (120).

It is an unprimeable number.

It is a polite number, since it can be written in 23 ways as a sum of consecutive naturals, for example, 79927 + ... + 80873.

Almost surely, 2^76138800 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 76138800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (123899808).

76138800 is an abundant number, since it is smaller than the sum of its proper divisors (171660816).

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

76138800 is a wasteful number, since it uses less digits than its factorization.

76138800 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 1035 (or 1024 counting only the distinct ones).

The product of its (nonzero) digits is 8064, while the sum is 33.

The square root of 76138800 is about 8725.7549816620. The cubic root of 76138800 is about 423.8400666533.

The spelling of 76138800 in words is "seventy-six million, one hundred thirty-eight thousand, eight hundred".