78732 has 30 divisors (see below), whose sum is σ = 206668. Its totient is φ = 26244.

The previous prime is 78721. The next prime is 78737. The reversal of 78732 is 23787.

It is a powerful number, because all its prime factors have an exponent greater than 1 and also an Achilles number because it is not a perfect power.

It is a Harshad number since it is a multiple of its sum of digits (27).

It is a plaindrome in base 16.

It is a nialpdrome in base 3.

It is a zygodrome in base 3.

It is a junction number, because it is equal to *n*+sod(*n*) for *n* = 78696 and 78705.

It is not an unprimeable number, because it can be changed into a prime (78737) by changing a digit.

It is a polite number, since it can be written in 9 ways as a sum of consecutive naturals, for example, 26243 + 26244 + 26245.

78732 is a Friedman number, since it can be written as 3^8*(7+7-2), using all its digits and the basic arithmetic operations.

2^{78732} 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 78732, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (103334).

78732 is an abundant number, since it is smaller than the sum of its proper divisors (127936).

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

78732 is an frugal number, since it uses more digits than its factorization.

78732 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 31 (or 5 counting only the distinct ones).

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

The square root of 78732 is about 280.5922308262. The cubic root of 78732 is about 42.8598284031.

Multiplying 78732 by its sum of digits (27), we get a square (2125764 = 1458^{2}).

78732 divided by its sum of digits (27) gives a square (2916 = 54^{2}).

Multiplying 78732 by its product of digits (2352), we get a square (185177664 = 13608^{2}).

Subtracting from 78732 its reverse (23787), we obtain a palindrome (54945).

It can be divided in two parts, 7873 and 2, that added together give a triangular number (7875 = T_{125}).

The spelling of 78732 in words is "seventy-eight thousand, seven hundred thirty-two".

Divisors: 1 2 3 4 6 9 12 18 27 36 54 81 108 162 243 324 486 729 972 1458 2187 2916 4374 6561 8748 13122 19683 26244 39366 78732

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