684648 has 48 divisors (see below), whose sum is σ = 1911780. Its totient is φ = 221184.

The previous prime is 684647. The next prime is 684683. The reversal of 684648 is 846486.

684648 = 54³ + 55³ + ... + 57³.

684648 is a `hidden beast` number, since 6 + 8 + 4 + 648 = 666.

It can be written as a sum of positive squares in 2 ways, for example, as 492804 + 191844 = 702^2 + 438^2 .

It is a Smith number, since the sum of its digits (36) coincides with the sum of the digits of its prime factors.

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 not an unprimeable number, because it can be changed into a prime (684643) by changing a digit.

It is a polite number, since it can be written in 11 ways as a sum of consecutive naturals, for example, 2536 + ... + 2792.

2⁶⁸⁴⁶⁴⁸ is an apocalyptic number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 684648, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (955890).

684648 is an abundant number, since it is smaller than the sum of its proper divisors (1227132).

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

684648 is a wasteful number, since it uses less digits than its factorization.

684648 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 306 (or 299 counting only the distinct ones).

The product of its digits is 36864, while the sum is 36.

The square root of 684648 is about 827.4345895598. The cubic root of 684648 is about 88.1364961613.

The spelling of 684648 in words is "six hundred eighty-four thousand, six hundred forty-eight".