78132 has 24 divisors (see below), whose sum is σ = 193536. Its totient is φ = 24448.

The previous prime is 78121. The next prime is 78137. The reversal of 78132 is 23187.

It is a super-2 number, since 2×78132² = 12209218848, which contains 22 as substring.

It is a junction number, because it is equal to n+sod(n) for n = 78099 and 78108.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (78137) by changing a digit.

78132 is an untouchable number, because it is not equal to the sum of proper divisors of any 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 7 ways as a sum of consecutive naturals, for example, 13 + ... + 395.

It is an arithmetic number, because the mean of its divisors is an integer number (8064).

78132 is a Friedman number, since it can be written as 8+(3+2)^7-1, using all its digits and the basic arithmetic operations.

2⁷⁸¹³² 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 78132, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (96768).

78132 is an abundant number, since it is smaller than the sum of its proper divisors (115404).

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

78132 is a wasteful number, since it uses less digits than its factorization.

78132 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 407 (or 405 counting only the distinct ones).

The product of its digits is 336, while the sum is 21.

The square root of 78132 is about 279.5210188877. The cubic root of 78132 is about 42.7506754108.

Subtracting from 78132 its reverse (23187), we obtain a palindrome (54945).

It can be divided in two parts, 78 and 132, that multiplied together give a triangular number (10296 = T₁₄₃).

The spelling of 78132 in words is "seventy-eight thousand, one hundred thirty-two".