688920 has 32 divisors (see below), whose sum is σ = 2067120. Its totient is φ = 183680.

The previous prime is 688907. The next prime is 688939. The reversal of 688920 is 29886.

688920 = T₁₅₂ + T₁₅₃ + ... + T₁₉₆.

It is a super-2 number, since 2×688920² = 949221532800, which contains 22 as substring.

It is a congruent number.

It is an unprimeable number.

688920 is an untouchable number, because it is not equal to the sum of proper divisors of any number.

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 7 ways as a sum of consecutive naturals, for example, 2751 + ... + 2990.

2⁶⁸⁸⁹²⁰ is an apocalyptic number.

688920 is a gapful number since it is divisible by the number (60) formed by its first and last digit.

It is an amenable number.

688920 is an abundant number, since it is smaller than the sum of its proper divisors (1378200).

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

688920 is a wasteful number, since it uses less digits than its factorization.

688920 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 5755 (or 5751 counting only the distinct ones).

The product of its (nonzero) digits is 6912, while the sum is 33.

The square root of 688920 is about 830.0120481053. The cubic root of 688920 is about 88.3194313789.

The spelling of 688920 in words is "six hundred eighty-eight thousand, nine hundred twenty".