681984 has 72 divisors (see below), whose sum is σ = 2022930. Its totient is φ = 221184.

The previous prime is 681983. The next prime is 681997. The reversal of 681984 is 489186.

It is a happy number.

It can be written as a sum of positive squares in only one way, i.e., 451584 + 230400 = 672^2 + 480^2 .

It is a tau number, because it is divible by the number of its divisors (72).

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

It is a nude number because it is divisible by every one of its digits.

It is an inconsummate number, since it does not exist a number n which divided by its sum of digits gives 681984.

It is not an unprimeable number, because it can be changed into a prime (681983) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (5) of ones.

It is a polite number, since it can be written in 5 ways as a sum of consecutive naturals, for example, 18414 + ... + 18450.

2⁶⁸¹⁹⁸⁴ is an apocalyptic number.

681984 is a gapful number since it is divisible by the number (64) 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 681984, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (1011465).

681984 is an abundant number, since it is smaller than the sum of its proper divisors (1340946).

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

681984 is a wasteful number, since it uses less digits than its factorization.

681984 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 65 (or 42 counting only the distinct ones).

The product of its digits is 13824, while the sum is 36.

The square root of 681984 is about 825.8232256361. The cubic root of 681984 is about 88.0220330505.

It can be divided in two parts, 6819 and 84, that added together give a triangular number (6903 = T₁₁₇).

The spelling of 681984 in words is "six hundred eighty-one thousand, nine hundred eighty-four".