405972000 has 480 divisors, whose sum is σ = 1712430720. Its totient is φ = 92275200.

The previous prime is 405971989. The next prime is 405972023. The reversal of 405972000 is 279504.

It is a tau number, because it is divible by the number of its divisors (480).

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

It is an unprimeable number.

It is a polite number, since it can be written in 79 ways as a sum of consecutive naturals, for example, 2267911 + ... + 2268089.

It is an arithmetic number, because the mean of its divisors is an integer number (3567564).

Almost surely, 2^405972000 is an apocalyptic number.

405972000 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 405972000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (856215360).

405972000 is an abundant number, since it is smaller than the sum of its proper divisors (1306458720).

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

405972000 is a wasteful number, since it uses less digits than its factorization.

405972000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 223 (or 196 counting only the distinct ones).

The product of its (nonzero) digits is 2520, while the sum is 27.

The square root of 405972000 is about 20148.7468592962. The cubic root of 405972000 is about 740.4550403146.

The spelling of 405972000 in words is "four hundred five million, nine hundred seventy-two thousand".