752064000 has 160 divisors (see below), whose sum is σ = 2501063136. Its totient is φ = 200499200.

The previous prime is 752063993. The next prime is 752064007. The reversal of 752064000 is 460257.

It is a happy number.

It is an interprime number because it is at equal distance from previous prime (752063993) and next prime (752064007).

It is a tau number, because it is divible by the number of its divisors (160).

It is a Harshad number since it is a multiple of its sum of digits (24).

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (752064007) by changing a digit.

It is a polite number, since it can be written in 15 ways as a sum of consecutive naturals, for example, 190042 + ... + 193958.

Almost surely, 2^752064000 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 752064000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (1250531568).

752064000 is an abundant number, since it is smaller than the sum of its proper divisors (1748999136).

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

752064000 is an equidigital number, since it uses as much as digits as its factorization.

752064000 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 3953 (or 3927 counting only the distinct ones).

The product of its (nonzero) digits is 1680, while the sum is 24.

The square root of 752064000 is about 27423.7852967091. The cubic root of 752064000 is about 909.3929856742.

The spelling of 752064000 in words is "seven hundred fifty-two million, sixty-four thousand".