414121200 has 120 divisors (see below), whose sum is σ = 1331300208. Its totient is φ = 110039040.

The previous prime is 414121163. The next prime is 414121217. The reversal of 414121200 is 2121414.

It is a tau number, because it is divible by the number of its divisors (120).

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 414121200.

It is a congruent number.

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (17) of ones.

It is a polite number, since it can be written in 23 ways as a sum of consecutive naturals, for example, 519202 + ... + 519998.

Almost surely, 2^414121200 is an apocalyptic number.

414121200 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 414121200, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (665650104).

414121200 is an abundant number, since it is smaller than the sum of its proper divisors (917179008).

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

414121200 is a wasteful number, since it uses less digits than its factorization.

414121200 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 1251 (or 1240 counting only the distinct ones).

The product of its (nonzero) digits is 64, while the sum is 15.

The square root of 414121200 is about 20349.9680589430. The cubic root of 414121200 is about 745.3767144238.

Adding to 414121200 its reverse (2121414), we get a palindrome (416242614).

The spelling of 414121200 in words is "four hundred fourteen million, one hundred twenty-one thousand, two hundred".