688392900 has 216 divisors, whose sum is σ = 2461108104. Its totient is φ = 159436800.

The previous prime is 688392893. The next prime is 688392931. The reversal of 688392900 is 9293886.

It can be written as a sum of positive squares in 12 ways, for example, as 316057284 + 372335616 = 17778^2 + 19296^2 .

It is a Harshad number since it is a multiple of its sum of digits (45).

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 71 ways as a sum of consecutive naturals, for example, 197170 + ... + 200630.

It is an arithmetic number, because the mean of its divisors is an integer number (11394019).

Almost surely, 2^688392900 is an apocalyptic number.

688392900 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 688392900, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (1230554052).

688392900 is an abundant number, since it is smaller than the sum of its proper divisors (1772715204).

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

688392900 is a wasteful number, since it uses less digits than its factorization.

688392900 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 3511 (or 3501 counting only the distinct ones).

The product of its (nonzero) digits is 186624, while the sum is 45.

The square root of 688392900 is about 26237.2426142687. The cubic root of 688392900 is about 882.9690092057.

The spelling of 688392900 in words is "six hundred eighty-eight million, three hundred ninety-two thousand, nine hundred".