420405984 has 96 divisors (see below), whose sum is σ = 1229921280. Its totient is φ = 139708800.

The previous prime is 420405977. The next prime is 420406001. The reversal of 420405984 is 489504024.

420405984 is a `hidden beast` number, since 4 + 20 + 40 + 598 + 4 = 666.

It is a tau number, because it is divible by the number of its divisors (96).

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

It is a congruent number.

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (13) of ones.

It is a polite number, since it can be written in 15 ways as a sum of consecutive naturals, for example, 423729 + ... + 424719.

It is an arithmetic number, because the mean of its divisors is an integer number (12811680).

Almost surely, 2^420405984 is an apocalyptic number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 420405984, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (614960640).

420405984 is an abundant number, since it is smaller than the sum of its proper divisors (809515296).

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

420405984 is a wasteful number, since it uses less digits than its factorization.

420405984 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 1501 (or 1487 counting only the distinct ones).

The product of its (nonzero) digits is 46080, while the sum is 36.

The square root of 420405984 is about 20503.8041348429. The cubic root of 420405984 is about 749.1284596154.

The spelling of 420405984 in words is "four hundred twenty million, four hundred five thousand, nine hundred eighty-four".