13734864000 has 1536 divisors, whose sum is σ = 62553254400. Its totient is φ = 2838528000.

The previous prime is 13734863993. The next prime is 13734864007. The reversal of 13734864000 is 46843731.

13734864000 is a `hidden beast` number, since 1 + 3 + 7 + 3 + 4 + 8 + 640 + 0 + 0 = 666.

It is an interprime number because it is at equal distance from previous prime (13734863993) and next prime (13734864007).

It is a Harshad number since it is a multiple of its sum of digits (36).

It is not an unprimeable number, because it can be changed into a prime (13734864007) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (13) of ones.

It is a polite number, since it can be written in 191 ways as a sum of consecutive naturals, for example, 473615986 + ... + 473616014.

It is an arithmetic number, because the mean of its divisors is an integer number (40724775).

Almost surely, 2^13734864000 is an apocalyptic number.

13734864000 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 13734864000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (31276627200).

13734864000 is an abundant number, since it is smaller than the sum of its proper divisors (48818390400).

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

13734864000 is a wasteful number, since it uses less digits than its factorization.

13734864000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 111 (or 86 counting only the distinct ones).

The product of its (nonzero) digits is 48384, while the sum is 36.

The spelling of 13734864000 in words is "thirteen billion, seven hundred thirty-four million, eight hundred sixty-four thousand".