413516400 has 120 divisors (see below), whose sum is σ = 1445097984. Its totient is φ = 100243200.

The previous prime is 413516359. The next prime is 413516417. The reversal of 413516400 is 4615314.

It is a tau number, because it is divible by the number of its divisors (120).

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

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 23 ways as a sum of consecutive naturals, for example, 2464 + ... + 28863.

Almost surely, 2^413516400 is an apocalyptic number.

413516400 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 413516400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (722548992).

413516400 is an abundant number, since it is smaller than the sum of its proper divisors (1031581584).

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

413516400 is a wasteful number, since it uses less digits than its factorization.

413516400 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 31359 (or 31348 counting only the distinct ones).

The product of its (nonzero) digits is 1440, while the sum is 24.

The square root of 413516400 is about 20335.1026552609. The cubic root of 413516400 is about 745.0136778114.

The spelling of 413516400 in words is "four hundred thirteen million, five hundred sixteen thousand, four hundred".