84672 has 84 divisors (see below), whose sum is σ = 289560. Its totient is φ = 24192.

The previous prime is 84659. The next prime is 84673. The reversal of 84672 is 27648.

It is a powerful number, because all its prime factors have an exponent greater than 1 and also an Achilles number because it is not a perfect power.

84672 is nontrivially palindromic in base 11.

It is a tau number, because it is divible by the number of its divisors (84).

It is a Harshad number since it is a multiple of its sum of digits (27).

It is a nude number because it is divisible by every one of its digits.

It is one of the 548 Lynch-Bell numbers.

Its product of digits (2688) is a multiple of the sum of its prime divisors (12).

It is a nialpdrome in base 12.

It is not an unprimeable number, because it can be changed into a prime (84673) by changing a digit.

It is a polite number, since it can be written in 11 ways as a sum of consecutive naturals, for example, 12093 + ... + 12099.

84672 is a Friedman number, since it can be written as 84^(6/2)/7, using all its digits and the basic arithmetic operations.

2⁸⁴⁶⁷² 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 84672, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (144780).

84672 is an abundant number, since it is smaller than the sum of its proper divisors (204888).

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

84672 is a wasteful number, since it uses less digits than its factorization.

84672 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 35 (or 12 counting only the distinct ones).

The product of its digits is 2688, while the sum is 27.

The square root of 84672 is about 290.9845356716. The cubic root of 84672 is about 43.9116685203.

Multiplying 84672 by its sum of digits (27), we get a square (2286144 = 1512²).

84672 divided by its sum of digits (27) gives a square (3136 = 56²).

Multiplying 84672 by its reverse (27648), we get a square (2341011456 = 48384²).

The spelling of 84672 in words is "eighty-four thousand, six hundred seventy-two".