753948000 has 480 divisors, whose sum is σ = 2996753760. Its totient is φ = 184550400.

The previous prime is 753947963. The next prime is 753948029. The reversal of 753948000 is 849357.

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 (36).

It is a congruent number.

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 79 ways as a sum of consecutive naturals, for example, 4211911 + ... + 4212089.

It is an arithmetic number, because the mean of its divisors is an integer number (6243237).

Almost surely, 2^753948000 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 753948000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (1498376880).

753948000 is an abundant number, since it is smaller than the sum of its proper divisors (2242805760).

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

753948000 is a wasteful number, since it uses less digits than its factorization.

753948000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 229 (or 202 counting only the distinct ones).

The product of its (nonzero) digits is 30240, while the sum is 36.

The square root of 753948000 is about 27458.1135550132. The cubic root of 753948000 is about 910.1517277094.

It can be divided in two parts, 753 and 948000, that added together give a triangular number (948753 = T₁₃₇₇).

The spelling of 753948000 in words is "seven hundred fifty-three million, nine hundred forty-eight thousand".