419973120 has 576 divisors, whose sum is σ = 1792627200. Its totient is φ = 92897280.

The previous prime is 419973109. The next prime is 419973121. The reversal of 419973120 is 21379914.

It is a tau number, because it is divible by the number of its divisors (576).

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

It is not an unprimeable number, because it can be changed into a prime (419973121) 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, 13547505 + ... + 13547535.

It is an arithmetic number, because the mean of its divisors is an integer number (3112200).

Almost surely, 2^419973120 is an apocalyptic number.

419973120 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 419973120, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (896313600).

419973120 is an abundant number, since it is smaller than the sum of its proper divisors (1372654080).

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

419973120 is a wasteful number, since it uses less digits than its factorization.

419973120 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 81 (or 48 counting only the distinct ones).

The product of its (nonzero) digits is 13608, while the sum is 36.

The square root of 419973120 is about 20493.2457165770. The cubic root of 419973120 is about 748.8712621199.

The spelling of 419973120 in words is "four hundred nineteen million, nine hundred seventy-three thousand, one hundred twenty".