414950400 has 198 divisors, whose sum is σ = 1486543682. Its totient is φ = 110592000.

The previous prime is 414950377. The next prime is 414950477. The reversal of 414950400 is 4059414.

It can be written as a sum of positive squares in 3 ways, for example, as 746496 + 414203904 = 864^2 + 20352^2 .

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (11) of ones.

It is a polite number, since it can be written in 17 ways as a sum of consecutive naturals, for example, 229500 + ... + 231300.

Almost surely, 2^414950400 is an apocalyptic number.

414950400 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 414950400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (743271841).

414950400 is an abundant number, since it is smaller than the sum of its proper divisors (1071593282).

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

414950400 is a wasteful number, since it uses less digits than its factorization.

414950400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 1837 (or 1811 counting only the distinct ones).

The product of its (nonzero) digits is 2880, while the sum is 27.

The square root of 414950400 is about 20370.3313669660. The cubic root of 414950400 is about 745.8738750854.

The spelling of 414950400 in words is "four hundred fourteen million, nine hundred fifty thousand, four hundred".