420384 has 48 divisors (see below), whose sum is σ = 1149120. Its totient is φ = 134400.

The previous prime is 420383. The next prime is 420397. The reversal of 420384 is 483024.

It is a happy number.

420384 is digitally balanced in base 3, because in such base it contains all the possibile digits an equal number of times.

It is a tau number, because it is divible by the number of its divisors (48).

It is a self number, because there is not a number n which added to its sum of digits gives 420384.

It is not an unprimeable number, because it can be changed into a prime (420383) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (7) of ones.

It is a polite number, since it can be written in 7 ways as a sum of consecutive naturals, for example, 2709 + ... + 2859.

It is an arithmetic number, because the mean of its divisors is an integer number (23940).

2⁴²⁰³⁸⁴ 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 420384, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (574560).

420384 is an abundant number, since it is smaller than the sum of its proper divisors (728736).

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

420384 is a wasteful number, since it uses less digits than its factorization.

420384 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 193 (or 185 counting only the distinct ones).

The product of its (nonzero) digits is 768, while the sum is 21.

The square root of 420384 is about 648.3702645865. The cubic root of 420384 is about 74.9115401502.

The spelling of 420384 in words is "four hundred twenty thousand, three hundred eighty-four".