428688000 has 384 divisors, whose sum is σ = 1665190800. Its totient is φ = 105062400.

The previous prime is 428687993. The next prime is 428688011. The reversal of 428688000 is 886824.

It can be written as a sum of positive squares in 8 ways, for example, as 25160256 + 403527744 = 5016^2 + 20088^2 .

It is a tau number, because it is divible by the number of its divisors (384).

It is a Harshad number since it is a multiple of its sum of digits (36).

It is an unprimeable number.

It is a polite number, since it can be written in 47 ways as a sum of consecutive naturals, for example, 1871886 + ... + 1872114.

Almost surely, 2^428688000 is an apocalyptic number.

428688000 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 428688000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (832595400).

428688000 is an abundant number, since it is smaller than the sum of its proper divisors (1236502800).

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

428688000 is a wasteful number, since it uses less digits than its factorization.

428688000 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 277 (or 252 counting only the distinct ones).

The product of its (nonzero) digits is 24576, while the sum is 36.

The square root of 428688000 is about 20704.7820563270. The cubic root of 428688000 is about 754.0157928336.

The spelling of 428688000 in words is "four hundred twenty-eight million, six hundred eighty-eight thousand".