472416 has 96 divisors (see below), whose sum is σ = 1532160. Its totient is φ = 124416.

The previous prime is 472411. The next prime is 472421. The reversal of 472416 is 614274.

It is an interprime number because it is at equal distance from previous prime (472411) and next prime (472421).

It is a tau number, because it is divible by the number of its divisors (96).

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.

472416 is an undulating number in base 11.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (472411) by changing a digit.

It is a polite number, since it can be written in 15 ways as a sum of consecutive naturals, for example, 12750 + ... + 12786.

It is an arithmetic number, because the mean of its divisors is an integer number (15960).

2⁴⁷²⁴¹⁶ 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 472416, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (766080).

472416 is an abundant number, since it is smaller than the sum of its proper divisors (1059744).

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

472416 is a wasteful number, since it uses less digits than its factorization.

472416 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 76 (or 68 counting only the distinct ones).

The product of its digits is 1344, while the sum is 24.

The square root of 472416 is about 687.3252505183. The cubic root of 472416 is about 77.8827957039.

It can be divided in two parts, 472 and 416, that added together give a palindrome (888).

The spelling of 472416 in words is "four hundred seventy-two thousand, four hundred sixteen".