45864000 has 504 divisors, whose sum is σ = 205529688. Its totient is φ = 9676800.

The previous prime is 45863989. The next prime is 45864029. The reversal of 45864000 is 46854.

It can be written as a sum of positive squares in 4 ways, for example, as 7225344 + 38638656 = 2688^2 + 6216^2 .

It is a tau number, because it is divible by the number of its divisors (504).

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 71 ways as a sum of consecutive naturals, for example, 3527994 + ... + 3528006.

It is an arithmetic number, because the mean of its divisors is an integer number (407797).

Almost surely, 2^45864000 is an apocalyptic number.

45864000 is a gapful number since it is divisible by the number (40) 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 45864000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (102764844).

45864000 is an abundant number, since it is smaller than the sum of its proper divisors (159665688).

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

45864000 is a wasteful number, since it uses less digits than its factorization.

45864000 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 60 (or 30 counting only the distinct ones).

The product of its (nonzero) digits is 3840, while the sum is 27.

The square root of 45864000 is about 6772.2965085708. The cubic root of 45864000 is about 357.9513265704.

The spelling of 45864000 in words is "forty-five million, eight hundred sixty-four thousand".