407988000 has 288 divisors, whose sum is σ = 1655821440. Its totient is φ = 93196800.

The previous prime is 407987977. The next prime is 407988013. The reversal of 407988000 is 889704.

It is a tau number, because it is divible by the number of its divisors (288).

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

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 47 ways as a sum of consecutive naturals, for example, 251191 + ... + 252809.

It is an arithmetic number, because the mean of its divisors is an integer number (5749380).

Almost surely, 2^407988000 is an apocalyptic number.

407988000 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 407988000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (827910720).

407988000 is an abundant number, since it is smaller than the sum of its proper divisors (1247833440).

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

407988000 is a wasteful number, since it uses less digits than its factorization.

407988000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 1657 (or 1636 counting only the distinct ones).

The product of its (nonzero) digits is 16128, while the sum is 36.

The square root of 407988000 is about 20198.7128302771. The cubic root of 407988000 is about 741.6786823510.

The spelling of 407988000 in words is "four hundred seven million, nine hundred eighty-eight thousand".