63648000 has 432 divisors, whose sum is σ = 261149616. Its totient is φ = 14745600.

The previous prime is 63647993. The next prime is 63648007. The reversal of 63648000 is 84636.

It is an interprime number because it is at equal distance from previous prime (63647993) and next prime (63648007).

It can be written as a sum of positive squares in 8 ways, for example, as 23503104 + 40144896 = 4848^2 + 6336^2 .

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (63648007) 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, 3743992 + ... + 3744008.

It is an arithmetic number, because the mean of its divisors is an integer number (604513).

Almost surely, 2^63648000 is an apocalyptic number.

63648000 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 63648000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (130574808).

63648000 is an abundant number, since it is smaller than the sum of its proper divisors (197501616).

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

63648000 is a wasteful number, since it uses less digits than its factorization.

63648000 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 67 (or 40 counting only the distinct ones).

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

The square root of 63648000 is about 7977.9696665254. The cubic root of 63648000 is about 399.2653180991.

The spelling of 63648000 in words is "sixty-three million, six hundred forty-eight thousand".