67766400 has 288 divisors, whose sum is σ = 261845220. Its totient is φ = 16588800.

The previous prime is 67766333. The next prime is 67766401. The reversal of 67766400 is 466776.

67766400 is a `hidden beast` number, since 6 + 7 + 7 + 6 + 640 + 0 = 666.

It can be written as a sum of positive squares in 6 ways, for example, as 788544 + 66977856 = 888^2 + 8184^2 .

It is a tau number, because it is divible by the number of its divisors (288).

It is a Harshad number since it is a multiple of its sum of digits (36).

It is not an unprimeable number, because it can be changed into a prime (67766401) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (5) of ones.

It is a polite number, since it can be written in 35 ways as a sum of consecutive naturals, for example, 374310 + ... + 374490.

Almost surely, 2^67766400 is an apocalyptic number.

67766400 is a gapful number since it is divisible by the number (60) 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 67766400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (130922610).

67766400 is an abundant number, since it is smaller than the sum of its proper divisors (194078820).

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

67766400 is a wasteful number, since it uses less digits than its factorization.

67766400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 224 (or 204 counting only the distinct ones).

The product of its (nonzero) digits is 42336, while the sum is 36.

The square root of 67766400 is about 8232.0349853484. The cubic root of 67766400 is about 407.6975844357.

The spelling of 67766400 in words is "sixty-seven million, seven hundred sixty-six thousand, four hundred".