419628000 has 432 divisors, whose sum is σ = 1605148272. Its totient is φ = 95744000.

The previous prime is 419627993. The next prime is 419628037. The reversal of 419628000 is 826914.

It is a Harshad number since it is a multiple of its sum of digits (30).

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 71 ways as a sum of consecutive naturals, for example, 24683992 + ... + 24684008.

It is an arithmetic number, because the mean of its divisors is an integer number (3715621).

Almost surely, 2^419628000 is an apocalyptic number.

419628000 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 419628000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (802574136).

419628000 is an abundant number, since it is smaller than the sum of its proper divisors (1185520272).

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

419628000 is a wasteful number, since it uses less digits than its factorization.

419628000 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 84 (or 38 counting only the distinct ones).

The product of its (nonzero) digits is 3456, while the sum is 30.

The square root of 419628000 is about 20484.8236506932. The cubic root of 419628000 is about 748.6660733706. Note that the first 3 decimals are identical.

Multiplying 419628000 by its sum of digits (30), we get a square (12588840000 = 112200²).

419628000 divided by its sum of digits (30) gives a square (13987600 = 3740²).

The spelling of 419628000 in words is "four hundred nineteen million, six hundred twenty-eight thousand".