414214400 has 108 divisors (see below), whose sum is σ = 1043034804. Its totient is φ = 162816000.

The previous prime is 414214387. The next prime is 414214403. The reversal of 414214400 is 4412414.

It is a happy number.

It can be written as a sum of positive squares in 6 ways, for example, as 52301824 + 361912576 = 7232^2 + 19024^2 .

It is a Harshad number since it is a multiple of its sum of digits (20).

It is not an unprimeable number, because it can be changed into a prime (414214403) by changing a digit.

It is a polite number, since it can be written in 11 ways as a sum of consecutive naturals, for example, 389870 + ... + 390930.

Almost surely, 2^414214400 is an apocalyptic number.

414214400 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 414214400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (521517402).

414214400 is an abundant number, since it is smaller than the sum of its proper divisors (628820404).

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

414214400 is a wasteful number, since it uses less digits than its factorization.

414214400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 1148 (or 1129 counting only the distinct ones).

The product of its (nonzero) digits is 512, while the sum is 20.

The square root of 414214400 is about 20352.2578600017. The cubic root of 414214400 is about 745.4326271204.

Adding to 414214400 its reverse (4412414), we get a palindrome (418626814).

The spelling of 414214400 in words is "four hundred fourteen million, two hundred fourteen thousand, four hundred".