415200 has 72 divisors (see below), whose sum is σ = 1359288. Its totient is φ = 110080.

The previous prime is 415189. The next prime is 415201. The reversal of 415200 is 2514.

415200 is digitally balanced in base 3, because in such base it contains all the possibile digits an equal number of times.

It is a Harshad number since it is a multiple of its sum of digits (12).

It is a congruent number.

It is an inconsummate number, since it does not exist a number n which divided by its sum of digits gives 415200.

It is not an unprimeable number, because it can be changed into a prime (415201) by changing a digit.

415200 is an untouchable number, because it is not equal to the sum of proper divisors of any number.

It is a polite number, since it can be written in 11 ways as a sum of consecutive naturals, for example, 2314 + ... + 2486.

It is an arithmetic number, because the mean of its divisors is an integer number (18879).

2⁴¹⁵²⁰⁰ is an apocalyptic number.

415200 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 415200, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (679644).

415200 is an abundant number, since it is smaller than the sum of its proper divisors (944088).

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

415200 is a wasteful number, since it uses less digits than its factorization.

415200 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 196 (or 183 counting only the distinct ones).

The product of its (nonzero) digits is 40, while the sum is 12.

The square root of 415200 is about 644.3601477435. The cubic root of 415200 is about 74.6023397216.

Adding to 415200 its reverse (2514), we get a palindrome (417714).

Subtracting from 415200 its reverse (2514), we obtain a triangular number (412686 = T₉₀₈).

The spelling of 415200 in words is "four hundred fifteen thousand, two hundred".