432378000 has 400 divisors, whose sum is σ = 1664183664. Its totient is φ = 107827200.

The previous prime is 432377993. The next prime is 432378047. The reversal of 432378000 is 873234.

It can be written as a sum of positive squares in 8 ways, for example, as 123743376 + 308634624 = 11124^2 + 17568^2 .

It is a tau number, because it is divible by the number of its divisors (400).

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

It is a congruent number.

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (11) of ones.

It is a polite number, since it can be written in 79 ways as a sum of consecutive naturals, for example, 2753922 + ... + 2754078.

Almost surely, 2^432378000 is an apocalyptic number.

432378000 is a gapful number since it is divisible by the number (40) 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 432378000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (832091832).

432378000 is an abundant number, since it is smaller than the sum of its proper divisors (1231805664).

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

432378000 is a wasteful number, since it uses less digits than its factorization.

432378000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 209 (or 184 counting only the distinct ones).

The product of its (nonzero) digits is 4032, while the sum is 27.

The square root of 432378000 is about 20793.7009692839. The cubic root of 432378000 is about 756.1730518434.

The spelling of 432378000 in words is "four hundred thirty-two million, three hundred seventy-eight thousand".