77440406400 has 1152 divisors, whose sum is σ = 336450965760. Its totient is φ = 17219174400.

The previous prime is 77440406377. The next prime is 77440406401. The reversal of 77440406400 is 460404477.

77440406400 is a `hidden beast` number, since 7 + 7 + 4 + 4 + 0 + 4 + 0 + 640 + 0 = 666.

It is a tau number, because it is divible by the number of its divisors (1152).

It is a hoax number, since the sum of its digits (36) coincides with the sum of the digits of its distinct prime factors.

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 (77440406401) 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, 223171027 + ... + 223171373.

It is an arithmetic number, because the mean of its divisors is an integer number (292058130).

Almost surely, 2^77440406400 is an apocalyptic number.

77440406400 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 77440406400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (168225482880).

77440406400 is an abundant number, since it is smaller than the sum of its proper divisors (259010559360).

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

77440406400 is a wasteful number, since it uses less digits than its factorization.

77440406400 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 434 (or 405 counting only the distinct ones).

The product of its (nonzero) digits is 75264, while the sum is 36.

The spelling of 77440406400 in words is "seventy-seven billion, four hundred forty million, four hundred six thousand, four hundred".