7505616038400 has 1200 divisors, whose sum is σ = 28822893335808. Its totient is φ = 1936933171200.

The previous prime is 7505616038377. The next prime is 7505616038407. The reversal of 7505616038400 is 48306165057.

It is a powerful number, because all its prime factors have an exponent greater than 1 and also an Achilles number because it is not a perfect power.

7505616038400 is a `hidden beast` number, since 7 + 5 + 0 + 56 + 160 + 38 + 400 = 666.

It is a tau number, because it is divible by the number of its divisors (1200).

It is a Harshad number since it is a multiple of its sum of digits (45).

It is not an unprimeable number, because it can be changed into a prime (7505616038407) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (19) of ones.

It is a polite number, since it can be written in 119 ways as a sum of consecutive naturals, for example, 242116646385 + ... + 242116646415.

Almost surely, 2^{7505616038400} is an apocalyptic number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 7505616038400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (14411446667904).

7505616038400 is an abundant number, since it is smaller than the sum of its proper divisors (21317277297408).

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

7505616038400 is an frugal number, since it uses more digits than its factorization.

7505616038400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 148 (or 41 counting only the distinct ones).

The product of its (nonzero) digits is 604800, while the sum is 45.

The spelling of 7505616038400 in words is "seven trillion, five hundred five billion, six hundred sixteen million, thirty-eight thousand, four hundred".