13205306400 has 576 divisors, whose sum is σ = 51105479040. Its totient is φ = 2919628800.

The previous prime is 13205306399. The next prime is 13205306441. The reversal of 13205306400 is 460350231.

It is a happy number.

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

It is an unprimeable number.

It is a polite number, since it can be written in 95 ways as a sum of consecutive naturals, for example, 37408624 + ... + 37408976.

It is an arithmetic number, because the mean of its divisors is an integer number (88724790).

Almost surely, 2^13205306400 is an apocalyptic number.

13205306400 is a gapful number since it is divisible by the number (10) 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 13205306400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (25552739520).

13205306400 is an abundant number, since it is smaller than the sum of its proper divisors (37900172640).

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

13205306400 is a wasteful number, since it uses less digits than its factorization.

13205306400 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 509 (or 496 counting only the distinct ones).

The product of its (nonzero) digits is 2160, while the sum is 24.

Adding to 13205306400 its reverse (460350231), we get a palindrome (13665656631).

The spelling of 13205306400 in words is "thirteen billion, two hundred five million, three hundred six thousand, four hundred".