414000 has 120 divisors (see below), whose sum is σ = 1508832. Its totient is φ = 105600.

The previous prime is 413981. The next prime is 414013. The reversal of 414000 is 414.

414000 = 123² + 124² + ... + 145².

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 (9).

It is a super Niven number, because it is divisible the sum of any subset of its (nonzero) digits.

It is an unprimeable number.

414000 is an untouchable number, because it is not equal to the sum of proper divisors of any number.

It is a pernicious number, because its binary representation contains a prime number (7) of ones.

It is a polite number, since it can be written in 23 ways as a sum of consecutive naturals, for example, 17989 + ... + 18011.

2⁴¹⁴⁰⁰⁰ is an apocalyptic number.

414000 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 414000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (754416).

414000 is an abundant number, since it is smaller than the sum of its proper divisors (1094832).

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

414000 is a wasteful number, since it uses less digits than its factorization.

414000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 52 (or 33 counting only the distinct ones).

The product of its (nonzero) digits is 16, while the sum is 9.

The square root of 414000 is about 643.4283176858. The cubic root of 414000 is about 74.5303991372.

Adding to 414000 its reverse (414), we get a palindrome (414414).

414000 divided by its reverse (414) gives a cube (1000 = 10³).

The spelling of 414000 in words is "four hundred fourteen thousand", and thus it is an iban number.