687852000 has 480 divisors, whose sum is σ = 2768429664. Its totient is φ = 165888000.

The previous prime is 687851993. The next prime is 687852001. The reversal of 687852000 is 258786.

687852000 is a `hidden beast` number, since 68 + 78 + 520 + 0 + 0 = 666.

It is a tau number, because it is divible by the number of its divisors (480).

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

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (687852001) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (17) of ones.

It is a polite number, since it can be written in 79 ways as a sum of consecutive naturals, for example, 3563904 + ... + 3564096.

Almost surely, 2^687852000 is an apocalyptic number.

687852000 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 687852000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (1384214832).

687852000 is an abundant number, since it is smaller than the sum of its proper divisors (2080577664).

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

687852000 is a wasteful number, since it uses less digits than its factorization.

687852000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 241 (or 214 counting only the distinct ones).

The product of its (nonzero) digits is 26880, while the sum is 36.

The square root of 687852000 is about 26226.9327219178. The cubic root of 687852000 is about 882.7376863273.

The spelling of 687852000 in words is "six hundred eighty-seven million, eight hundred fifty-two thousand".