77312334310400 has 1056 divisors, whose sum is σ = 239536305838080. Its totient is φ = 24138712350720.

The previous prime is 77312334310327. The next prime is 77312334310411. The reversal of 77312334310400 is 401343321377.

It is a super-3 number, since 3×77312334310400³ (a number of 43 digits) contains 333 as substring.

It is an unprimeable number.

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 95 ways as a sum of consecutive naturals, for example, 12743088167 + ... + 12743094233.

Almost surely, 2^{77312334310400} is an apocalyptic number.

77312334310400 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 77312334310400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (119768152919040).

77312334310400 is an abundant number, since it is smaller than the sum of its proper divisors (162223971527680).

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

77312334310400 is a wasteful number, since it uses less digits than its factorization.

77312334310400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 6257 (or 6234 counting only the distinct ones).

The product of its (nonzero) digits is 127008, while the sum is 38.

Adding to 77312334310400 its reverse (401343321377), we get a palindrome (77713677631777).

The spelling of 77312334310400 in words is "seventy-seven trillion, three hundred twelve billion, three hundred thirty-four million, three hundred ten thousand, four hundred".