77786561638800 has 960 divisors, whose sum is σ = 336264706252800. Its totient is φ = 16672092364800.

The previous prime is 77786561638781. The next prime is 77786561638813. The reversal of 77786561638800 is 883616568777.

It is a Harshad number since it is a multiple of its sum of digits (72).

It is an unprimeable number.

It is a polite number, since it can be written in 191 ways as a sum of consecutive naturals, for example, 348177531 + ... + 348400869.

It is an arithmetic number, because the mean of its divisors is an integer number (350275735680).

Almost surely, 2^{77786561638800} is an apocalyptic number.

77786561638800 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 77786561638800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (168132353126400).

77786561638800 is an abundant number, since it is smaller than the sum of its proper divisors (258478144614000).

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

77786561638800 is a wasteful number, since it uses less digits than its factorization.

77786561638800 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 223661 (or 223644 counting only the distinct ones).

The product of its (nonzero) digits is 568995840, while the sum is 72.

The spelling of 77786561638800 in words is "seventy-seven trillion, seven hundred eighty-six billion, five hundred sixty-one million, six hundred thirty-eight thousand, eight hundred".