83872 has 12 divisors (see below), whose sum is σ = 165186. Its totient is φ = 41920.

The previous prime is 83869. The next prime is 83873. The reversal of 83872 is 27838.

It is a happy number.

It can be written as a sum of positive squares in only one way, i.e., 59536 + 24336 = 244^2 + 156^2 .

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

It is a plaindrome in base 14.

It is a self number, because there is not a number n which added to its sum of digits gives 83872.

It is not an unprimeable number, because it can be changed into a prime (83873) by changing a digit.

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 as a sum of consecutive naturals, namely, 1279 + ... + 1342.

2⁸³⁸⁷² is an apocalyptic number.

It is an amenable number.

83872 is a deficient number, since it is larger than the sum of its proper divisors (81314).

83872 is a wasteful number, since it uses less digits than its factorization.

83872 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 2631 (or 2623 counting only the distinct ones).

The product of its digits is 2688, while the sum is 28.

The square root of 83872 is about 289.6066297584. The cubic root of 83872 is about 43.7729349136.

It can be divided in two parts, 8 and 3872, that multiplied together give a square (30976 = 176²).

The spelling of 83872 in words is "eighty-three thousand, eight hundred seventy-two".