84768 has 24 divisors (see below), whose sum is σ = 222768. Its totient is φ = 28224.

The previous prime is 84761. The next prime is 84787. The reversal of 84768 is 86748.

It is a tau number, because it is divible by the number of its divisors (24).

It is a super-2 number, since 2×84768² = 14371227648, which contains 22 as substring.

Its product of digits (10752) is a multiple of the sum of its prime factors (896).

It is an inconsummate number, since it does not exist a number n which divided by its sum of digits gives 84768.

It is not an unprimeable number, because it can be changed into a prime (84761) by changing a digit.

84768 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 3 ways as a sum of consecutive naturals, for example, 346 + ... + 537.

It is an arithmetic number, because the mean of its divisors is an integer number (9282).

2⁸⁴⁷⁶⁸ is an apocalyptic number.

It is an amenable number.

84768 is an abundant number, since it is smaller than the sum of its proper divisors (138000).

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

It is a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (111384).

84768 is a wasteful number, since it uses less digits than its factorization.

84768 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 896 (or 888 counting only the distinct ones).

The product of its digits is 10752, while the sum is 33.

The square root of 84768 is about 291.1494461612. The cubic root of 84768 is about 43.9282577431.

The spelling of 84768 in words is "eighty-four thousand, seven hundred sixty-eight".