63684000 has 288 divisors, whose sum is σ = 237641040. Its totient is φ = 16128000.

The previous prime is 63683933. The next prime is 63684001. The reversal of 63684000 is 48636.

It can be written as a sum of positive squares in 8 ways, for example, as 767376 + 62916624 = 876^2 + 7932^2 .

It is a tau number, because it is divible by the number of its divisors (288).

It is not an unprimeable number, because it can be changed into a prime (63684001) by changing a digit.

It is a polite number, since it can be written in 47 ways as a sum of consecutive naturals, for example, 1043970 + ... + 1044030.

Almost surely, 2^63684000 is an apocalyptic number.

63684000 is a gapful number since it is divisible by the number (60) 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 63684000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (118820520).

63684000 is an abundant number, since it is smaller than the sum of its proper divisors (173957040).

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

63684000 is a wasteful number, since it uses less digits than its factorization.

63684000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 121 (or 100 counting only the distinct ones).

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

The square root of 63684000 is about 7980.2255607220. The cubic root of 63684000 is about 399.3405801778.

The spelling of 63684000 in words is "sixty-three million, six hundred eighty-four thousand".