663768 has 64 divisors (see below), whose sum is σ = 2112000. Its totient is φ = 189216.

The previous prime is 663763. The next prime is 663787. The reversal of 663768 is 867366.

It is a happy number.

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 a congruent number.

It is not an unprimeable number, because it can be changed into a prime (663763) by changing a digit.

663768 is an untouchable number, because it is not equal to the sum of proper divisors of any number.

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, 1293 + ... + 1731.

It is an arithmetic number, because the mean of its divisors is an integer number (33000).

2⁶⁶³⁷⁶⁸ 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 663768, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (1056000).

663768 is an abundant number, since it is smaller than the sum of its proper divisors (1448232).

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

663768 is a wasteful number, since it uses less digits than its factorization.

663768 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 461 (or 451 counting only the distinct ones).

The product of its digits is 36288, while the sum is 36.

The square root of 663768 is about 814.7195836605. The cubic root of 663768 is about 87.2312515990.

It can be divided in two parts, 663 and 768, that added together give a triangular number (1431 = T₅₃).

The spelling of 663768 in words is "six hundred sixty-three thousand, seven hundred sixty-eight".