414214000 has 80 divisors (see below), whose sum is σ = 1016024256. Its totient is φ = 163296000.

The previous prime is 414213991. The next prime is 414214039. The reversal of 414214000 is 412414.

It is a tau number, because it is divible by the number of its divisors (80).

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

It is a congruent number.

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 15 ways as a sum of consecutive naturals, for example, 140542 + ... + 143458.

Almost surely, 2^414214000 is an apocalyptic number.

414214000 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 414214000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (508012128).

414214000 is an abundant number, since it is smaller than the sum of its proper divisors (601810256).

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

414214000 is a wasteful number, since it uses less digits than its factorization.

414214000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 3011 (or 2995 counting only the distinct ones).

The product of its (nonzero) digits is 128, while the sum is 16.

The square root of 414214000 is about 20352.2480330798. The cubic root of 414214000 is about 745.4323871697.

Adding to 414214000 its reverse (412414), we get a palindrome (414626414).

The spelling of 414214000 in words is "four hundred fourteen million, two hundred fourteen thousand".