77968800 has 648 divisors, whose sum is σ = 364687596. Its totient is φ = 15482880.

The previous prime is 77968763. The next prime is 77968801. The reversal of 77968800 is 886977.

It can be written as a sum of positive squares in 6 ways, for example, as 24561936 + 53406864 = 4956^2 + 7308^2 .

It is a Harshad number since it is a multiple of its sum of digits (45).

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (77968801) by changing a digit.

It is a polite number, since it can be written in 107 ways as a sum of consecutive naturals, for example, 4586392 + ... + 4586408.

Almost surely, 2^77968800 is an apocalyptic number.

77968800 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 77968800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (182343798).

77968800 is an abundant number, since it is smaller than the sum of its proper divisors (286718796).

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

77968800 is a wasteful number, since it uses less digits than its factorization.

77968800 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 70 (or 47 counting only the distinct ones).

The product of its (nonzero) digits is 169344, while the sum is 45.

The square root of 77968800 is about 8829.9943374840. The cubic root of 77968800 is about 427.2088917898.

The spelling of 77968800 in words is "seventy-seven million, nine hundred sixty-eight thousand, eight hundred".