81672 has 32 divisors (see below), whose sum is σ = 211680. Its totient is φ = 26240.

The previous prime is 81671. The next prime is 81677. The reversal of 81672 is 27618.

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

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

It is an inconsummate number, since it does not exist a number n which divided by its sum of digits gives 81672.

It is not an unprimeable number, because it can be changed into a prime (81671) by changing a digit.

It is a polite number, since it can be written in 7 ways as a sum of consecutive naturals, for example, 943 + ... + 1025.

It is an arithmetic number, because the mean of its divisors is an integer number (6615).

2⁸¹⁶⁷² is an apocalyptic number.

81672 is a gapful number since it is divisible by the number (82) formed by its first and last digit.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 81672, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (105840).

81672 is an abundant number, since it is smaller than the sum of its proper divisors (130008).

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

81672 is a wasteful number, since it uses less digits than its factorization.

81672 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 133 (or 129 counting only the distinct ones).

The product of its digits is 672, while the sum is 24.

The square root of 81672 is about 285.7831345619. The cubic root of 81672 is about 43.3868110306.

81672 divided by its sum of digits (24) gives a triangular number (3403 = T₈₂).

It can be divided in two parts, 816 and 72, that added together give a palindrome (888).

The spelling of 81672 in words is "eighty-one thousand, six hundred seventy-two".