413314200 has 288 divisors, whose sum is σ = 1584273600. Its totient is φ = 95662080.

The previous prime is 413314199. The next prime is 413314241. The reversal of 413314200 is 2413314.

It is a Harshad number since it is a multiple of its sum of digits (18).

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 71 ways as a sum of consecutive naturals, for example, 397281 + ... + 398319.

It is an arithmetic number, because the mean of its divisors is an integer number (5500950).

Almost surely, 2^413314200 is an apocalyptic number.

413314200 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 413314200, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (792136800).

413314200 is an abundant number, since it is smaller than the sum of its proper divisors (1170959400).

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

413314200 is a wasteful number, since it uses less digits than its factorization.

413314200 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 1091 (or 1079 counting only the distinct ones).

The product of its (nonzero) digits is 288, while the sum is 18.

The square root of 413314200 is about 20330.1303488197. The cubic root of 413314200 is about 744.8922265012.

Adding to 413314200 its reverse (2413314), we get a palindrome (415727514).

The spelling of 413314200 in words is "four hundred thirteen million, three hundred fourteen thousand, two hundred".