76128000 has 288 divisors, whose sum is σ = 276773952. Its totient is φ = 18432000.

The previous prime is 76127993. The next prime is 76128007. The reversal of 76128000 is 82167.

It is an interprime number because it is at equal distance from previous prime (76127993) and next prime (76128007).

It is a Harshad number since it is a multiple of its sum of digits (24).

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (76128007) by changing a digit.

It is a polite number, since it can be written in 31 ways as a sum of consecutive naturals, for example, 1247970 + ... + 1248030.

Almost surely, 2^76128000 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 76128000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (138386976).

76128000 is an abundant number, since it is smaller than the sum of its proper divisors (200645952).

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

76128000 is a wasteful number, since it uses less digits than its factorization.

76128000 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 108 (or 84 counting only the distinct ones).

The product of its (nonzero) digits is 672, while the sum is 24.

The square root of 76128000 is about 8725.1361020903. The cubic root of 76128000 is about 423.8200256704.

The spelling of 76128000 in words is "seventy-six million, one hundred twenty-eight thousand".