3413264400 has 960 divisors, whose sum is σ = 15705661440. Its totient is φ = 684288000.

The previous prime is 3413264383. The next prime is 3413264411. The reversal of 3413264400 is 44623143.

3413264400 is a `hidden beast` number, since 3 + 4 + 13 + 2 + 644 + 0 + 0 = 666.

It is a Harshad number since it is a multiple of its sum of digits (27).

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 191 ways as a sum of consecutive naturals, for example, 22604325 + ... + 22604475.

It is an arithmetic number, because the mean of its divisors is an integer number (16360064).

Almost surely, 2^3413264400 is an apocalyptic number.

3413264400 is a gapful number since it is divisible by the number (30) 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 3413264400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (7852830720).

3413264400 is an abundant number, since it is smaller than the sum of its proper divisors (12292397040).

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

3413264400 is a wasteful number, since it uses less digits than its factorization.

3413264400 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 221 (or 204 counting only the distinct ones).

The product of its (nonzero) digits is 6912, while the sum is 27.

The square root of 3413264400 is about 58423.1495214012. The cubic root of 3413264400 is about 1505.6475103992.

Adding to 3413264400 its reverse (44623143), we get a palindrome (3457887543).

The spelling of 3413264400 in words is "three billion, four hundred thirteen million, two hundred sixty-four thousand, four hundred".