688560 has 80 divisors (see below), whose sum is σ = 2261760. Its totient is φ = 172800.

The previous prime is 688543. The next prime is 688561. The reversal of 688560 is 65886.

It is a tau number, because it is divible by the number of its divisors (80).

It is a super-2 number, since 2×688560² = 948229747200, which contains 22 as substring.

It is a Smith number, since the sum of its digits (33) coincides with the sum of the digits of its prime factors.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (688561) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (7) of ones.

It is a polite number, since it can be written in 15 ways as a sum of consecutive naturals, for example, 4485 + ... + 4635.

It is an arithmetic number, because the mean of its divisors is an integer number (28272).

2⁶⁸⁸⁵⁶⁰ is an apocalyptic number.

688560 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 688560, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (1130880).

688560 is an abundant number, since it is smaller than the sum of its proper divisors (1573200).

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

688560 is a wasteful number, since it uses less digits than its factorization.

688560 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 186 (or 180 counting only the distinct ones).

The product of its (nonzero) digits is 11520, while the sum is 33.

The square root of 688560 is about 829.7951554450. The cubic root of 688560 is about 88.3040447181.

The spelling of 688560 in words is "six hundred eighty-eight thousand, five hundred sixty".