432768 has 96 divisors (see below), whose sum is σ = 1395360. Its totient is φ = 118272.

The previous prime is 432749. The next prime is 432781. The reversal of 432768 is 867234.

It is a tau number, because it is divible by the number of its divisors (96).

It is a nude number because it is divisible by every one of its digits.

It is a d-powerful number, because it can be written as 4⁹ + 3⁸ + 7 + 2¹⁷ + 6³ + 8⁵ .

It is one of the 548 Lynch-Bell numbers.

It is a congruent number.

It is an inconsummate number, since it does not exist a number n which divided by its sum of digits gives 432768.

It is an unprimeable number.

432768 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 11 ways as a sum of consecutive naturals, for example, 18805 + ... + 18827.

It is an arithmetic number, because the mean of its divisors is an integer number (14535).

432768 is a Friedman number, since it can be written as 46*(8*7)^2*3, using all its digits and the basic arithmetic operations.

2⁴³²⁷⁶⁸ is an apocalyptic number.

432768 is a gapful number since it is divisible by the number (48) 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 432768, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (697680).

432768 is an abundant number, since it is smaller than the sum of its proper divisors (962592).

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

432768 is a wasteful number, since it uses less digits than its factorization.

432768 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 54 (or 35 counting only the distinct ones).

The product of its digits is 8064, while the sum is 30.

The square root of 432768 is about 657.8510469704. The cubic root of 432768 is about 75.6400336663.

It can be divided in two parts, 432 and 768, that multiplied together give a 4-th power (331776 = 24⁴).

The spelling of 432768 in words is "four hundred thirty-two thousand, seven hundred sixty-eight".