63504000 has 480 divisors, whose sum is σ = 274362660. Its totient is φ = 14515200.

The previous prime is 63503987. The next prime is 63504011. The reversal of 63504000 is 40536.

It is a happy number.

It is a powerful number, because all its prime factors have an exponent greater than 1 and also an Achilles number because it is not a perfect power.

63504000 is digitally balanced in base 2, because in such base it contains all the possibile digits an equal number of times.

It can be written as a sum of positive squares in 2 ways, for example, as 42928704 + 20575296 = 6552^2 + 4536^2 .

It is a tau number, because it is divible by the number of its divisors (480).

It is a Harshad number since it is a multiple of its sum of digits (18).

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (13) of ones.

It is a polite number, since it can be written in 59 ways as a sum of consecutive naturals, for example, 9071997 + ... + 9072003.

Almost surely, 2^63504000 is an apocalyptic number.

63504000 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 63504000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (137181330).

63504000 is an abundant number, since it is smaller than the sum of its proper divisors (210858660).

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

63504000 is an equidigital number, since it uses as much as digits as its factorization.

63504000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 55 (or 17 counting only the distinct ones).

The product of its (nonzero) digits is 360, while the sum is 18.

The square root of 63504000 is about 7968.9397036243. The cubic root of 63504000 is about 398.9639856691.

Multiplying 63504000 by its product of nonzero digits (360), we get a square (22861440000 = 151200²).

63504000 divided by its product of nonzero digits (360) gives a square (176400 = 420²).

Adding to 63504000 its reverse (40536), we get a palindrome (63544536).

The spelling of 63504000 in words is "sixty-three million, five hundred four thousand".