71728000 has 64 divisors (see below), whose sum is σ = 178373520. Its totient is φ = 28684800.

The previous prime is 71727979. The next prime is 71728039. The reversal of 71728000 is 82717.

71728000 = T₅ + T₆ + ... + T₇₅₄.

It is a happy number.

It is a tau number, because it is divible by the number of its divisors (64).

It is a Harshad number since it is a multiple of its sum of digits (25).

It is a congruent number.

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (11) of ones.

It is a polite number, since it can be written in 7 ways as a sum of consecutive naturals, for example, 13759 + ... + 18241.

Almost surely, 2^71728000 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 71728000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (89186760).

71728000 is an abundant number, since it is smaller than the sum of its proper divisors (106645520).

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

71728000 is an equidigital number, since it uses as much as digits as its factorization.

71728000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 4512 (or 4490 counting only the distinct ones).

The product of its (nonzero) digits is 784, while the sum is 25.

The square root of 71728000 is about 8469.2384545483. The cubic root of 71728000 is about 415.4922305676.

The spelling of 71728000 in words is "seventy-one million, seven hundred twenty-eight thousand".