414344400 has 240 divisors, whose sum is σ = 1480708800. Its totient is φ = 98426880.

The previous prime is 414344393. The next prime is 414344461. The reversal of 414344400 is 4443414.

It is a tau number, because it is divible by the number of its divisors (240).

It is a super-2 number, since 2×414344400² = 343362563622720000, which contains 22 as substring.

It is a Harshad number since it is a multiple of its sum of digits (24).

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 47 ways as a sum of consecutive naturals, for example, 387066 + ... + 388134.

It is an arithmetic number, because the mean of its divisors is an integer number (6169620).

Almost surely, 2^414344400 is an apocalyptic number.

414344400 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 414344400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (740354400).

414344400 is an abundant number, since it is smaller than the sum of its proper divisors (1066364400).

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

414344400 is a wasteful number, since it uses less digits than its factorization.

414344400 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 1126 (or 1115 counting only the distinct ones).

The product of its (nonzero) digits is 3072, while the sum is 24.

The square root of 414344400 is about 20355.4513582971. The cubic root of 414344400 is about 745.5106029266.

Adding to 414344400 its reverse (4443414), we get a palindrome (418787814).

The spelling of 414344400 in words is "four hundred fourteen million, three hundred forty-four thousand, four hundred".