78432 has 48 divisors (see below), whose sum is σ = 221760. Its totient is φ = 24192.

The previous prime is 78427. The next prime is 78437. The reversal of 78432 is 23487.

78432 is nontrivially palindromic in base 7.

It is an interprime number because it is at equal distance from previous prime (78427) and next prime (78437).

It is a tau number, because it is divible by the number of its divisors (48).

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

It is a d-powerful number, because it can be written as 7⁵ + 8³ + 4² + 3¹⁰ + 2¹¹ .

78432 is a nontrivial repdigit in base 7.

It is a plaindrome in base 7.

It is a nialpdrome in base 7.

It is a zygodrome in base 7.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (78437) 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, 1803 + ... + 1845.

It is an arithmetic number, because the mean of its divisors is an integer number (4620).

2⁷⁸⁴³² 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 78432, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (110880).

78432 is an abundant number, since it is smaller than the sum of its proper divisors (143328).

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

78432 is a wasteful number, since it uses less digits than its factorization.

78432 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 75 (or 67 counting only the distinct ones).

The product of its digits is 1344, while the sum is 24.

The square root of 78432 is about 280.0571370274. The cubic root of 78432 is about 42.8053214916.

Subtracting from 78432 its reverse (23487), we obtain a palindrome (54945).

The spelling of 78432 in words is "seventy-eight thousand, four hundred thirty-two".