• 684 can be written using four 4's:

See also 113.

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684 has 18 divisors (see below), whose sum is σ = 1820. Its totient is φ = 216.

The previous prime is 683. The next prime is 691. The reversal of 684 is 486.

684 = 5³ + 6³ + 7³.

684 is digitally balanced in base 2 and base 3, because in such bases it contains all the possibile digits an equal number of times.

It is a tau number, because it is divible by the number of its divisors (18).

It is a Harshad number since it is a multiple of its sum of digits (18).

Its product of digits (192) is a multiple of the sum of its prime divisors (24).

It is a plaindrome in base 14 and base 16.

It is a nialpdrome in base 3, base 6 and base 9.

It is a zygodrome in base 3.

It is not an unprimeable number, because it can be changed into a prime (683) 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, 27 + ... + 45.

2⁶⁸⁴ 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 684, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (910).

684 is an abundant number, since it is smaller than the sum of its proper divisors (1136).

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

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

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

The sum of its prime factors is 29 (or 24 counting only the distinct ones).

The product of its digits is 192, while the sum is 18.

The square root of 684 is about 26.1533936612. The cubic root of 684 is about 8.8108681149.

Subtracting from 684 its sum of digits (18), we obtain a palindrome (666).

Multiplying 684 by its product of digits (192), we get a triangular number (131328 = T₅₁₂).

It can be divided in two parts, 68 and 4, that multiplied together give a palindrome (272).

The spelling of 684 in words is "six hundred eighty-four", and thus it is an aban number.