63648 has 72 divisors (see below), whose sum is σ = 206388. Its totient is φ = 18432.

The previous prime is 63647. The next prime is 63649. The reversal of 63648 is 84636.

It is an interprime number because it is at equal distance from previous prime (63647) and next prime (63649).

It can be written as a sum of positive squares in 2 ways, for example, as 63504 + 144 = 252^2 + 12^2 .

It is a tau number, because it is divible by the number of its divisors (72).

It is a nude number because it is divisible by every one of its digits.

It is an Ulam number.

It is a congruent number.

It is an inconsummate number, since it does not exist a number n which divided by its sum of digits gives 63648.

It is not an unprimeable number, because it can be changed into a prime (63647) 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 11 ways as a sum of consecutive naturals, for example, 3736 + ... + 3752.

2⁶³⁶⁴⁸ is an apocalyptic number.

63648 is a gapful number since it is divisible by the number (68) 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 63648, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (103194).

63648 is an abundant number, since it is smaller than the sum of its proper divisors (142740).

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

63648 is a wasteful number, since it uses less digits than its factorization.

63648 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 46 (or 35 counting only the distinct ones).

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

The square root of 63648 is about 252.2855524995. The cubic root of 63648 is about 39.9265318099.

The spelling of 63648 in words is "sixty-three thousand, six hundred forty-eight".