84072 has 32 divisors (see below), whose sum is σ = 218880. Its totient is φ = 26880.

The previous prime is 84067. The next prime is 84089. The reversal of 84072 is 27048.

It is a happy number.

It is an inconsummate number, since it does not exist a number n which divided by its sum of digits gives 84072.

It is an unprimeable number.

84072 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 7 ways as a sum of consecutive naturals, for example, 688 + ... + 800.

It is an arithmetic number, because the mean of its divisors is an integer number (6840).

2⁸⁴⁰⁷² 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 84072, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (109440).

84072 is an abundant number, since it is smaller than the sum of its proper divisors (134808).

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

84072 is a wasteful number, since it uses less digits than its factorization.

84072 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 153 (or 149 counting only the distinct ones).

The product of its (nonzero) digits is 448, while the sum is 21.

The square root of 84072 is about 289.9517201191. The cubic root of 84072 is about 43.8077007373.

The spelling of 84072 in words is "eighty-four thousand, seventy-two".