76128 has 48 divisors (see below), whose sum is σ = 218736. Its totient is φ = 23040.

The previous prime is 76123. The next prime is 76129. The reversal of 76128 is 82167.

It is a tau number, because it is divible by the number of its divisors (48).

It is a Smith number, since the sum of its digits (24) coincides with the sum of the digits of its prime factors.

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

It is a junction number, because it is equal to n+sod(n) for n = 76098 and 76107.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (76123) by changing a digit.

It is a polite number, since it can be written in 7 ways as a sum of consecutive naturals, for example, 1218 + ... + 1278.

It is an arithmetic number, because the mean of its divisors is an integer number (4557).

2⁷⁶¹²⁸ is an apocalyptic number.

76128 is a gapful number since it is divisible by the number (78) 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 76128, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (109368).

76128 is an abundant number, since it is smaller than the sum of its proper divisors (142608).

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

76128 is a wasteful number, since it uses less digits than its factorization.

76128 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 87 (or 79 counting only the distinct ones).

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

The square root of 76128 is about 275.9130297757. The cubic root of 76128 is about 42.3820025670.

The spelling of 76128 in words is "seventy-six thousand, one hundred twenty-eight".