414101400 has 96 divisors (see below), whose sum is σ = 1286822400. Its totient is φ = 110160000.

The previous prime is 414101341. The next prime is 414101431. The reversal of 414101400 is 4101414.

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 414101400.

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 23 ways as a sum of consecutive naturals, for example, 450141 + ... + 451059.

It is an arithmetic number, because the mean of its divisors is an integer number (13404400).

Almost surely, 2^414101400 is an apocalyptic number.

414101400 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 414101400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (643411200).

414101400 is an abundant number, since it is smaller than the sum of its proper divisors (872721000).

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

414101400 is a wasteful number, since it uses less digits than its factorization.

414101400 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 1689 (or 1680 counting only the distinct ones).

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

The square root of 414101400 is about 20349.4815658778. The cubic root of 414101400 is about 745.3648348951.

Adding to 414101400 its reverse (4101414), we get a palindrome (418202814).

The spelling of 414101400 in words is "four hundred fourteen million, one hundred one thousand, four hundred".