419990400 has 192 divisors, whose sum is σ = 1537364400. Its totient is φ = 111974400.

The previous prime is 419990399. The next prime is 419990401. The reversal of 419990400 is 4099914.

It is an interprime number because it is at equal distance from previous prime (419990399) and next prime (419990401).

It is a tau number, because it is divible by the number of its divisors (192).

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

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (419990401) by changing a digit.

It is a polite number, since it can be written in 23 ways as a sum of consecutive naturals, for example, 83970 + ... + 88830.

Almost surely, 2^419990400 is an apocalyptic number.

419990400 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 419990400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (768682200).

419990400 is an abundant number, since it is smaller than the sum of its proper divisors (1117374000).

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

419990400 is a wasteful number, since it uses less digits than its factorization.

419990400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 4894 (or 4871 counting only the distinct ones).

The product of its (nonzero) digits is 11664, while the sum is 36.

The square root of 419990400 is about 20493.6673145633. The cubic root of 419990400 is about 748.8815328708.

The spelling of 419990400 in words is "four hundred nineteen million, nine hundred ninety thousand, four hundred".