45648000 has 192 divisors, whose sum is σ = 164450520. Its totient is φ = 12134400.

The previous prime is 45647977. The next prime is 45648007. The reversal of 45648000 is 84654.

It can be written as a sum of positive squares in 4 ways, for example, as 3968064 + 41679936 = 1992^2 + 6456^2 .

It is a tau number, because it is divible by the number of its divisors (192).

It is not an unprimeable number, because it can be changed into a prime (45648007) by changing a digit.

It is a polite number, since it can be written in 23 ways as a sum of consecutive naturals, for example, 143842 + ... + 144158.

Almost surely, 2^45648000 is an apocalyptic number.

45648000 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 45648000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (82225260).

45648000 is an abundant number, since it is smaller than the sum of its proper divisors (118802520).

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

45648000 is a wasteful number, since it uses less digits than its factorization.

45648000 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 352 (or 327 counting only the distinct ones).

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

The square root of 45648000 is about 6756.3303649244. The cubic root of 45648000 is about 357.3885090908.

It can be divided in two parts, 45 and 648000, that multiplied together give a square (29160000 = 5400²).

The spelling of 45648000 in words is "forty-five million, six hundred forty-eight thousand".