85072 has 20 divisors (see below), whose sum is σ = 177940. Its totient is φ = 39168.

The previous prime is 85061. The next prime is 85081. The reversal of 85072 is 27058.

It can be written as a sum of positive squares in 2 ways, for example, as 46656 + 38416 = 216^2 + 196^2 .

It is an alternating number because its digits alternate between even and odd.

It is a congruent number.

It is an unprimeable number.

85072 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, 4 + ... + 412.

It is an arithmetic number, because the mean of its divisors is an integer number (8897).

2⁸⁵⁰⁷² 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 85072, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (88970).

85072 is an abundant number, since it is smaller than the sum of its proper divisors (92868).

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

85072 is a wasteful number, since it uses less digits than its factorization.

85072 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 430 (or 424 counting only the distinct ones).

The product of its (nonzero) digits is 560, while the sum is 22.

The square root of 85072 is about 291.6710475861. The cubic root of 85072 is about 43.9807077958.

The spelling of 85072 in words is "eighty-five thousand, seventy-two".