414352400 has 180 divisors, whose sum is σ = 1251544896. Its totient is φ = 129043200.

The previous prime is 414352397. The next prime is 414352403. The reversal of 414352400 is 4253414.

It is an interprime number because it is at equal distance from previous prime (414352397) and next prime (414352403).

It is a super-2 number, since 2×414352400² = 343375822771520000, which contains 22 as substring.

It is not an unprimeable number, because it can be changed into a prime (414352403) by changing a digit.

It is a polite number, since it can be written in 35 ways as a sum of consecutive naturals, for example, 338189 + ... + 339411.

Almost surely, 2^414352400 is an apocalyptic number.

414352400 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 414352400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (625772448).

414352400 is an abundant number, since it is smaller than the sum of its proper divisors (837192496).

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

414352400 is a wasteful number, since it uses less digits than its factorization.

414352400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 1270 (or 1248 counting only the distinct ones).

The product of its (nonzero) digits is 1920, while the sum is 23.

The square root of 414352400 is about 20355.6478649047. The cubic root of 414352400 is about 745.5154009050.

The spelling of 414352400 in words is "four hundred fourteen million, three hundred fifty-two thousand, four hundred".