84096 has 48 divisors (see below), whose sum is σ = 245310. Its totient is φ = 27648.

The previous prime is 84089. The next prime is 84121. The reversal of 84096 is 69048.

It can be written as a sum of positive squares in only one way, i.e., 69696 + 14400 = 264^2 + 120^2 .

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

It is an unprimeable number.

84096 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 5 ways as a sum of consecutive naturals, for example, 1116 + ... + 1188.

2⁸⁴⁰⁹⁶ 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 84096, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (122655).

84096 is an abundant number, since it is smaller than the sum of its proper divisors (161214).

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

84096 is a wasteful number, since it uses less digits than its factorization.

84096 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 93 (or 78 counting only the distinct ones).

The product of its (nonzero) digits is 1728, while the sum is 27.

The square root of 84096 is about 289.9931033663. The cubic root of 84096 is about 43.8118689296.

It can be divided in two parts, 8 and 4096, that multiplied together give a 15-th power (32768 = 2¹⁵).

The spelling of 84096 in words is "eighty-four thousand, ninety-six".