83772 has 36 divisors (see below), whose sum is σ = 229320. Its totient is φ = 25632.

The previous prime is 83761. The next prime is 83773. The reversal of 83772 is 27738.

It is a tau number, because it is divible by the number of its divisors (36).

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (83773) 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, 379 + ... + 557.

It is an arithmetic number, because the mean of its divisors is an integer number (6370).

2⁸³⁷⁷² 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 83772, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (114660).

83772 is an abundant number, since it is smaller than the sum of its proper divisors (145548).

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

83772 is a wasteful number, since it uses less digits than its factorization.

83772 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 202 (or 197 counting only the distinct ones).

The product of its digits is 2352, while the sum is 27.

The square root of 83772 is about 289.4339302846. The cubic root of 83772 is about 43.7555312734.

It can be divided in two parts, 837 and 72, that added together give a palindrome (909).

The spelling of 83772 in words is "eighty-three thousand, seven hundred seventy-two".