77696800 has 144 divisors (see below), whose sum is σ = 208814760. Its totient is φ = 28098560.

The previous prime is 77696779. The next prime is 77696803. The reversal of 77696800 is 869677.

It can be written as a sum of positive squares in 12 ways, for example, as 34715664 + 42981136 = 5892^2 + 6556^2 .

It is a hoax number, since the sum of its digits (43) coincides with the sum of the digits of its distinct prime factors.

It is not an unprimeable number, because it can be changed into a prime (77696803) by changing a digit.

It is a polite number, since it can be written in 23 ways as a sum of consecutive naturals, for example, 394302 + ... + 394498.

Almost surely, 2^77696800 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 77696800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (104407380).

77696800 is an abundant number, since it is smaller than the sum of its proper divisors (131117960).

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

77696800 is a wasteful number, since it uses less digits than its factorization.

77696800 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 263 (or 250 counting only the distinct ones).

The product of its (nonzero) digits is 127008, while the sum is 43.

The square root of 77696800 is about 8814.5788328201. The cubic root of 77696800 is about 426.7115295708.

The spelling of 77696800 in words is "seventy-seven million, six hundred ninety-six thousand, eight hundred".