13456800 has 288 divisors, whose sum is σ = 56246400. Its totient is φ = 3041280.

The previous prime is 13456799. The next prime is 13456811. The reversal of 13456800 is 865431.

It is a tau number, because it is divible by the number of its divisors (288).

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

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (11) of ones.

It is a polite number, since it can be written in 47 ways as a sum of consecutive naturals, for example, 151156 + ... + 151244.

It is an arithmetic number, because the mean of its divisors is an integer number (195300).

Almost surely, 2^13456800 is an apocalyptic number.

13456800 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 13456800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (28123200).

13456800 is an abundant number, since it is smaller than the sum of its proper divisors (42789600).

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

13456800 is a wasteful number, since it uses less digits than its factorization.

13456800 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 125 (or 106 counting only the distinct ones).

The product of its (nonzero) digits is 2880, while the sum is 27.

The square root of 13456800 is about 3668.3511282319. The cubic root of 13456800 is about 237.8559022278.

The spelling of 13456800 in words is "thirteen million, four hundred fifty-six thousand, eight hundred".