663984 has 80 divisors (see below), whose sum is σ = 2008800. Its totient is φ = 209664.

The previous prime is 663983. The next prime is 663991. The reversal of 663984 is 489366.

663984 = 40³ + 41³ + ... + 47³.

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 (663983) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (7) of ones.

It is a polite number, since it can be written in 15 ways as a sum of consecutive naturals, for example, 12502 + ... + 12554.

It is an arithmetic number, because the mean of its divisors is an integer number (25110).

663984 is a Friedman number, since it can be written as 8*6*(9+(6*4)^3), using all its digits and the basic arithmetic operations.

2⁶⁶³⁹⁸⁴ 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 663984, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (1004400).

663984 is an abundant number, since it is smaller than the sum of its proper divisors (1344816).

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

663984 is a wasteful number, since it uses less digits than its factorization.

663984 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 99 (or 87 counting only the distinct ones).

The product of its digits is 31104, while the sum is 36.

The square root of 663984 is about 814.8521338255. The cubic root of 663984 is about 87.2407126892.

The spelling of 663984 in words is "six hundred sixty-three thousand, nine hundred eighty-four".