414400 has 84 divisors (see below), whose sum is σ = 1196848. Its totient is φ = 138240.

The previous prime is 414397. The next prime is 414413. The reversal of 414400 is 4414.

It is a happy number.

It is an unprimeable number.

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 11 ways as a sum of consecutive naturals, for example, 11182 + ... + 11218.

2⁴¹⁴⁴⁰⁰ is an apocalyptic number.

414400 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 414400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (598424).

414400 is an abundant number, since it is smaller than the sum of its proper divisors (782448).

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

414400 is a wasteful number, since it uses less digits than its factorization.

414400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 66 (or 51 counting only the distinct ones).

The product of its (nonzero) digits is 64, while the sum is 13.

The square root of 414400 is about 643.7390775772. The cubic root of 414400 is about 74.5543947600.

Adding to 414400 its reverse (4414), we get a palindrome (418814).

It can be divided in two parts, 414 and 400, that multiplied together give a triangular number (165600 = T₅₇₅).

The spelling of 414400 in words is "four hundred fourteen thousand, four hundred", and thus it is an iban number.