74785513420800 has 4608 divisors, whose sum is σ = 354076537651200. Its totient is φ = 15049359360000.

The previous prime is 74785513420781. The next prime is 74785513420801. The reversal of 74785513420800 is 802431558747.

74785513420800 is a `hidden beast` number, since 7 + 4 + 7 + 8 + 5 + 513 + 42 + 0 + 80 + 0 = 666.

74785513420800 is digitally balanced in base 5, because in such base it contains all the possibile digits an equal number of times.

It is a tau number, because it is divible by the number of its divisors (4608).

It is a super-2 number, since 2×74785513420800² (a number of 29 digits) contains 22 as substring.

It is a Harshad number since it is a multiple of its sum of digits (54).

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (74785513420801) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (17) of ones.

It is a polite number, since it can be written in 383 ways as a sum of consecutive naturals, for example, 495268300725 + ... + 495268300875.

It is an arithmetic number, because the mean of its divisors is an integer number (76839526400).

Almost surely, 2^{74785513420800} is an apocalyptic number.

74785513420800 is a gapful number since it is divisible by the number (70) 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 74785513420800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (177038268825600).

74785513420800 is an abundant number, since it is smaller than the sum of its proper divisors (279291024230400).

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

74785513420800 is a wasteful number, since it uses less digits than its factorization.

74785513420800 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 370 (or 339 counting only the distinct ones).

The product of its (nonzero) digits is 7526400, while the sum is 54.

The spelling of 74785513420800 in words is "seventy-four trillion, seven hundred eighty-five billion, five hundred thirteen million, four hundred twenty thousand, eight hundred".