77768000 has 56 divisors (see below), whose sum is σ = 192612264. Its totient is φ = 31104000.

The previous prime is 77767997. The next prime is 77768011. The reversal of 77768000 is 86777.

It can be written as a sum of positive squares in 4 ways, for example, as 19642624 + 58125376 = 4432^2 + 7624^2 .

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 7 ways as a sum of consecutive naturals, for example, 3140 + ... + 12860.

Almost surely, 2^77768000 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 77768000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (96306132).

77768000 is an abundant number, since it is smaller than the sum of its proper divisors (114844264).

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

77768000 is an equidigital number, since it uses as much as digits as its factorization.

77768000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 9748 (or 9728 counting only the distinct ones).

The product of its (nonzero) digits is 16464, while the sum is 35.

The square root of 77768000 is about 8818.6166715648. The cubic root of 77768000 is about 426.8418334579.

The spelling of 77768000 in words is "seventy-seven million, seven hundred sixty-eight thousand".