677664000 has 432 divisors, whose sum is σ = 2640512784. Its totient is φ = 165888000.

The previous prime is 677663983. The next prime is 677664011. The reversal of 677664000 is 466776.

677664000 is a `hidden beast` number, since 6 + 7 + 7 + 6 + 640 + 0 + 0 = 666.

It can be written as a sum of positive squares in 8 ways, for example, as 559984896 + 117679104 = 23664^2 + 10848^2 .

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

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 47 ways as a sum of consecutive naturals, for example, 3743910 + ... + 3744090.

Almost surely, 2^677664000 is an apocalyptic number.

677664000 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 677664000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (1320256392).

677664000 is an abundant number, since it is smaller than the sum of its proper divisors (1962848784).

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

677664000 is a wasteful number, since it uses less digits than its factorization.

677664000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 231 (or 204 counting only the distinct ones).

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

The square root of 677664000 is about 26031.9803318918. The cubic root of 677664000 is about 878.3578189505.

The spelling of 677664000 in words is "six hundred seventy-seven million, six hundred sixty-four thousand".