414106000 has 160 divisors (see below), whose sum is σ = 1248848640. Its totient is φ = 129024000.

The previous prime is 414105997. The next prime is 414106019. The reversal of 414106000 is 601414.

It is a happy number.

It is a Harshad number since it is a multiple of its sum of digits (16).

It is an unprimeable number.

It is a polite number, since it can be written in 31 ways as a sum of consecutive naturals, for example, 152656 + ... + 155344.

It is an arithmetic number, because the mean of its divisors is an integer number (7805304).

Almost surely, 2^414106000 is an apocalyptic number.

414106000 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 414106000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (624424320).

414106000 is an abundant number, since it is smaller than the sum of its proper divisors (834742640).

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

414106000 is a wasteful number, since it uses less digits than its factorization.

414106000 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 2730 (or 2714 counting only the distinct ones).

The product of its (nonzero) digits is 96, while the sum is 16.

The square root of 414106000 is about 20349.5945905563. The cubic root of 414106000 is about 745.3675948193.

Adding to 414106000 its reverse (601414), we get a palindrome (414707414).

The spelling of 414106000 in words is "four hundred fourteen million, one hundred six thousand".