77438032142400 has 504 divisors, whose sum is σ = 277055906517000. Its totient is φ = 20513783808000.

The previous prime is 77438032142377. The next prime is 77438032142437. The reversal of 77438032142400 is 424123083477.

77438032142400 is a `hidden beast` number, since 7 + 7 + 4 + 3 + 80 + 321 + 4 + 240 + 0 = 666.

It can be written as a sum of positive squares in 12 ways, for example, as 32946606144 + 77405085536256 = 181512^2 + 8798016^2 .

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

It is an unprimeable number.

It is a polite number, since it can be written in 71 ways as a sum of consecutive naturals, for example, 1480596250 + ... + 1480648550.

Almost surely, 2^{77438032142400} 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 77438032142400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (138527953258500).

77438032142400 is an abundant number, since it is smaller than the sum of its proper divisors (199617874374600).

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

77438032142400 is a wasteful number, since it uses less digits than its factorization.

77438032142400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 53007 (or 52989 counting only the distinct ones).

The product of its (nonzero) digits is 903168, while the sum is 45.

The spelling of 77438032142400 in words is "seventy-seven trillion, four hundred thirty-eight billion, thirty-two million, one hundred forty-two thousand, four hundred".