414816 has 48 divisors (see below), whose sum is σ = 1134000. Its totient is φ = 132608.

The previous prime is 414809. The next prime is 414833. The reversal of 414816 is 618414.

It is a tau number, because it is divible by the number of its divisors (48).

It is a Harshad number since it is a multiple of its sum of digits (24).

It is a nude number because it is divisible by every one of its digits.

It is a congruent number.

It is an unprimeable number.

414816 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 7 ways as a sum of consecutive naturals, for example, 2710 + ... + 2858.

It is an arithmetic number, because the mean of its divisors is an integer number (23625).

2⁴¹⁴⁸¹⁶ is an apocalyptic number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 414816, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (567000).

414816 is an abundant number, since it is smaller than the sum of its proper divisors (719184).

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

414816 is a wasteful number, since it uses less digits than its factorization.

414816 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 191 (or 183 counting only the distinct ones).

The product of its digits is 768, while the sum is 24.

The square root of 414816 is about 644.0621088063. The cubic root of 414816 is about 74.5793338332.

The spelling of 414816 in words is "four hundred fourteen thousand, eight hundred sixteen".