405288000 has 336 divisors, whose sum is σ = 1564910256. Its totient is φ = 99532800.

The previous prime is 405287969. The next prime is 405288001. The reversal of 405288000 is 882504.

It can be written as a sum of positive squares in 8 ways, for example, as 295289856 + 109998144 = 17184^2 + 10488^2 .

It is not an unprimeable number, because it can be changed into a prime (405288001) by changing a digit.

It is a polite number, since it can be written in 47 ways as a sum of consecutive naturals, for example, 935784 + ... + 936216.

It is an arithmetic number, because the mean of its divisors is an integer number (4657471).

Almost surely, 2^405288000 is an apocalyptic number.

405288000 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 405288000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (782455128).

405288000 is an abundant number, since it is smaller than the sum of its proper divisors (1159622256).

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

405288000 is a wasteful number, since it uses less digits than its factorization.

405288000 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 479 (or 456 counting only the distinct ones).

The product of its (nonzero) digits is 2560, while the sum is 27.

The square root of 405288000 is about 20131.7659434040. The cubic root of 405288000 is about 740.0389558260.

It can be divided in two parts, 405 and 288000, that multiplied together give a square (116640000 = 10800²).

The spelling of 405288000 in words is "four hundred five million, two hundred eighty-eight thousand".