14468414400 has 1008 divisors, whose sum is σ = 61908537600. Its totient is φ = 3284582400.

The previous prime is 14468414377. The next prime is 14468414407. The reversal of 14468414400 is 441486441.

14468414400 is a `hidden beast` number, since 144 + 68 + 414 + 40 + 0 = 666.

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

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (14468414407) by changing a digit.

It is a polite number, since it can be written in 143 ways as a sum of consecutive naturals, for example, 72705501 + ... + 72705699.

It is an arithmetic number, because the mean of its divisors is an integer number (61417200).

Almost surely, 2^14468414400 is an apocalyptic number.

14468414400 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 14468414400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (30954268800).

14468414400 is an abundant number, since it is smaller than the sum of its proper divisors (47440123200).

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

14468414400 is a wasteful number, since it uses less digits than its factorization.

14468414400 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 264 (or 237 counting only the distinct ones).

The product of its (nonzero) digits is 49152, while the sum is 36.

The spelling of 14468414400 in words is "fourteen billion, four hundred sixty-eight million, four hundred fourteen thousand, four hundred".