85272 has 64 divisors (see below), whose sum is σ = 259200. Its totient is φ = 23040.

The previous prime is 85259. The next prime is 85297. The reversal of 85272 is 27258.

It is a Harshad number since it is a multiple of its sum of digits (24).

It is a d-powerful number, because it can be written as 8 + 5⁶ + 2¹² + 7 + 2¹⁶ .

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

Its product of digits (1120) is a multiple of the sum of its prime factors (56).

It is a congruent number.

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (7) of ones.

It is a polite number, since it can be written in 15 ways as a sum of consecutive naturals, for example, 4479 + ... + 4497.

It is an arithmetic number, because the mean of its divisors is an integer number (4050).

2⁸⁵²⁷² 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 85272, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (129600).

85272 is an abundant number, since it is smaller than the sum of its proper divisors (173928).

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

85272 is a wasteful number, since it uses less digits than its factorization.

85272 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 56 (or 52 counting only the distinct ones).

The product of its digits is 1120, while the sum is 24.

The square root of 85272 is about 292.0136983088. The cubic root of 85272 is about 44.0151463007.

85272 divided by its sum of digits (24) gives a palindrome (3553).

The spelling of 85272 in words is "eighty-five thousand, two hundred seventy-two".