677872800 has 432 divisors, whose sum is σ = 2712763872. Its totient is φ = 163814400.

The previous prime is 677872781. The next prime is 677872801. The reversal of 677872800 is 8278776.

It is a tau number, because it is divible by the number of its divisors (432).

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 (677872801) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (11) of ones.

It is a polite number, since it can be written in 71 ways as a sum of consecutive naturals, for example, 2138242 + ... + 2138558.

It is an arithmetic number, because the mean of its divisors is an integer number (6279546).

Almost surely, 2^677872800 is an apocalyptic number.

677872800 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 677872800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (1356381936).

677872800 is an abundant number, since it is smaller than the sum of its proper divisors (2034891072).

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

677872800 is a wasteful number, since it uses less digits than its factorization.

677872800 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 363 (or 338 counting only the distinct ones).

The product of its (nonzero) digits is 263424, while the sum is 45.

The square root of 677872800 is about 26035.9904747256. The cubic root of 677872800 is about 878.4480220991.

The spelling of 677872800 in words is "six hundred seventy-seven million, eight hundred seventy-two thousand, eight hundred".