414013200 has 60 divisors (see below), whose sum is σ = 1326226128. Its totient is φ = 110403200.

The previous prime is 414013183. The next prime is 414013219. The reversal of 414013200 is 2310414.

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 414013200.

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (13) of ones.

It is a polite number, since it can be written in 11 ways as a sum of consecutive naturals, for example, 171306 + ... + 173705.

Almost surely, 2^414013200 is an apocalyptic number.

414013200 is a gapful number since it is divisible by the number (40) formed by its first and last digit.

It is an amenable number.

414013200 is an abundant number, since it is smaller than the sum of its proper divisors (912212928).

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

414013200 is a wasteful number, since it uses less digits than its factorization.

414013200 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 345032 (or 345021 counting only the distinct ones).

The product of its (nonzero) digits is 96, while the sum is 15.

The square root of 414013200 is about 20347.3143190938. The cubic root of 414013200 is about 745.3119123931.

Adding to 414013200 its reverse (2310414), we get a palindrome (416323614).

The spelling of 414013200 in words is "four hundred fourteen million, thirteen thousand, two hundred".