76890 has 32 divisors (see below), whose sum is σ = 202176. Its totient is φ = 18560.

The previous prime is 76883. The next prime is 76907. The reversal of 76890 is 9867.

76890 = 122² + 123² + ... + 126².

It is a happy number.

It is a Harshad number since it is a multiple of its sum of digits (30).

It is an unprimeable number.

76890 is an untouchable number, because it is not equal to the sum of proper divisors of any number.

It is a polite number, since it can be written in 15 ways as a sum of consecutive naturals, for example, 214 + ... + 446.

It is an arithmetic number, because the mean of its divisors is an integer number (6318).

2⁷⁶⁸⁹⁰ is an apocalyptic number.

It is a practical number, because each smaller number is the sum of distinct divisors of 76890, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (101088).

76890 is an abundant number, since it is smaller than the sum of its proper divisors (125286).

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

76890 is a wasteful number, since it uses less digits than its factorization.

76890 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 254.

The product of its (nonzero) digits is 3024, while the sum is 30.

The square root of 76890 is about 277.2904614299. The cubic root of 76890 is about 42.5229403257.

It can be divided in two parts, 768 and 90, that added together give a palindrome (858).

The spelling of 76890 in words is "seventy-six thousand, eight hundred ninety".