416364 has 48 divisors (see below), whose sum is σ = 1114848. Its totient is φ = 119808.

The previous prime is 416359. The next prime is 416387. The reversal of 416364 is 463614.

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

Its product of digits (1728) is a multiple of the sum of its prime divisors (192).

It is an unprimeable number.

It is a polite number, since it can be written in 15 ways as a sum of consecutive naturals, for example, 2574 + ... + 2730.

It is an arithmetic number, because the mean of its divisors is an integer number (23226).

2⁴¹⁶³⁶⁴ 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 416364, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (557424).

416364 is an abundant number, since it is smaller than the sum of its proper divisors (698484).

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

416364 is a wasteful number, since it uses less digits than its factorization.

416364 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 194 (or 192 counting only the distinct ones).

The product of its digits is 1728, while the sum is 24.

The square root of 416364 is about 645.2627371854. The cubic root of 416364 is about 74.6719897707.

Adding to 416364 its reverse (463614), we get a palindrome (879978).

It can be divided in two parts, 416 and 364, that added together give a triangular number (780 = T₃₉).

The spelling of 416364 in words is "four hundred sixteen thousand, three hundred sixty-four".