73728000 has 204 divisors, whose sum is σ = 265811988. Its totient is φ = 19660800.

The previous prime is 73727981. The next prime is 73728019. The reversal of 73728000 is 82737.

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.

It is an interprime number because it is at equal distance from previous prime (73727981) and next prime (73728019).

It can be written as a sum of positive squares in 2 ways, for example, as 2359296 + 71368704 = 1536^2 + 8448^2 .

It is a congruent number.

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (5) of ones.

It is a polite number, since it can be written in 11 ways as a sum of consecutive naturals, for example, 14745598 + ... + 14745602.

Almost surely, 2^73728000 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 73728000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (132905994).

73728000 is an abundant number, since it is smaller than the sum of its proper divisors (192083988).

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

73728000 is an frugal number, since it uses more digits than its factorization.

73728000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 53 (or 10 counting only the distinct ones).

The product of its (nonzero) digits is 2352, while the sum is 27.

The square root of 73728000 is about 8586.5010335992. The cubic root of 73728000 is about 419.3186230734.

The spelling of 73728000 in words is "seventy-three million, seven hundred twenty-eight thousand".