419430400 has 75 divisors (see below), whose sum is σ = 1040187361. Its totient is φ = 167772160.

The previous prime is 419430383. The next prime is 419430419. The reversal of 419430400 is 4034914.

It is a happy number.

The square root of 419430400 is 20480.

It is a perfect power (a square), and thus also a powerful number.

419430400 is digitally balanced in base 6, because in such base it contains all the possibile digits an equal number of times.

It can be written as a sum of positive squares in only one way, i.e., 150994944 + 268435456 = 12288^2 + 16384^2 .

It is a Harshad number since it is a multiple of its sum of digits (25).

It is a Duffinian number.

It is a nialpdrome in base 8.

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (3) of ones.

It is a polite number, since it can be written in 2 ways as a sum of consecutive naturals, for example, 83886078 + ... + 83886082.

Almost surely, 2^419430400 is an apocalyptic number.

419430400 is a gapful number since it is divisible by the number (40) formed by its first and last digit.

419430400 is the 20480-th square number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 419430400

419430400 is an abundant number, since it is smaller than the sum of its proper divisors (620756961).

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

419430400 is an frugal number, since it uses more digits than its factorization.

419430400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 58 (or 7 counting only the distinct ones).

The product of its (nonzero) digits is 1728, while the sum is 25.

The cubic root of 419430400 is about 748.5485409825.

Multiplying 419430400 by its sum of digits (25), we get a 4-th power (10485760000 = 320⁴).

419430400 divided by its sum of digits (25) gives a 24-th power (16777216 = 2²⁴).

The spelling of 419430400 in words is "four hundred nineteen million, four hundred thirty thousand, four hundred".