77907648000 has 1200 divisors, whose sum is σ = 327208383216. Its totient is φ = 16437657600.

The previous prime is 77907647953. The next prime is 77907648001. The reversal of 77907648000 is 84670977.

It is a tau number, because it is divible by the number of its divisors (1200).

It is a Harshad number since it is a multiple of its sum of digits (48).

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (77907648001) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (13) of ones.

It is a polite number, since it can be written in 119 ways as a sum of consecutive naturals, for example, 5992895994 + ... + 5992896006.

Almost surely, 2^77907648000 is an apocalyptic number.

77907648000 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 77907648000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (163604191608).

77907648000 is an abundant number, since it is smaller than the sum of its proper divisors (249300735216).

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

77907648000 is an frugal number, since it uses more digits than its factorization.

77907648000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 90 (or 30 counting only the distinct ones).

The product of its (nonzero) digits is 592704, while the sum is 48.

The spelling of 77907648000 in words is "seventy-seven billion, nine hundred seven million, six hundred forty-eight thousand".