63684 has 36 divisors (see below), whose sum is σ = 169260. Its totient is φ = 20160.

The previous prime is 63671. The next prime is 63689. The reversal of 63684 is 48636.

63684 = T₁₉ + T₂₀ + ... + T₇₂.

63684 is digitally balanced in base 2, because in such base it contains all the possibile digits an equal number of times.

It can be written as a sum of positive squares in 2 ways, for example, as 14400 + 49284 = 120^2 + 222^2 .

It is a tau number, because it is divible by the number of its divisors (36).

It is not an unprimeable number, because it can be changed into a prime (63689) 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, 1014 + ... + 1074.

2⁶³⁶⁸⁴ 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 63684, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (84630).

63684 is an abundant number, since it is smaller than the sum of its proper divisors (105576).

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

63684 is a wasteful number, since it uses less digits than its factorization.

63684 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 100 (or 95 counting only the distinct ones).

The product of its digits is 3456, while the sum is 27.

The square root of 63684 is about 252.3568901378. The cubic root of 63684 is about 39.9340580178.

It can be divided in two parts, 63 and 684, that added together give a palindrome (747).

The spelling of 63684 in words is "sixty-three thousand, six hundred eighty-four".