414020400 has 60 divisors (see below), whose sum is σ = 1326249192. Its totient is φ = 110405120.

The previous prime is 414020389. The next prime is 414020413. The reversal of 414020400 is 4020414.

It is a tau number, because it is divible by the number of its divisors (60).

It is a Harshad number since it is a multiple of its sum of digits (15).

It is a self number, because there is not a number n which added to its sum of digits gives 414020400.

It is an unprimeable number.

It is a polite number, since it can be written in 11 ways as a sum of consecutive naturals, for example, 171309 + ... + 173708.

Almost surely, 2^414020400 is an apocalyptic number.

414020400 is a gapful number since it is divisible by the number (40) formed by its first and last digit.

It is an amenable number.

414020400 is an abundant number, since it is smaller than the sum of its proper divisors (912228792).

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

414020400 is a wasteful number, since it uses less digits than its factorization.

414020400 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 345038 (or 345027 counting only the distinct ones).

The product of its (nonzero) digits is 128, while the sum is 15.

The square root of 414020400 is about 20347.4912458514. The cubic root of 414020400 is about 745.3162328791.

Adding to 414020400 its reverse (4020414), we get a palindrome (418040814).

The spelling of 414020400 in words is "four hundred fourteen million, twenty thousand, four hundred".