45600 has 72 divisors (see below), whose sum is σ = 156240. Its totient is φ = 11520.

The previous prime is 45599. The next prime is 45613. The reversal of 45600 is 654.

45600 is nontrivially palindromic in base 7 and base 9.

It is a Harshad number since it is a multiple of its sum of digits (15).

It is a nialpdrome in base 16.

It is a self number, because there is not a number n which added to its sum of digits gives 45600.

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (5) of ones.

It is a polite number, since it can be written in 11 ways as a sum of consecutive naturals, for example, 2391 + ... + 2409.

It is an arithmetic number, because the mean of its divisors is an integer number (2170).

2⁴⁵⁶⁰⁰ is an apocalyptic number.

45600 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 45600, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (78120).

45600 is an abundant number, since it is smaller than the sum of its proper divisors (110640).

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

45600 is a wasteful number, since it uses less digits than its factorization.

45600 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 42 (or 29 counting only the distinct ones).

The product of its (nonzero) digits is 120, while the sum is 15.

The square root of 45600 is about 213.5415650406. The cubic root of 45600 is about 35.7263197542.

It can be divided in two parts, 45 and 600, that multiplied together give a cube (27000 = 30³).

The spelling of 45600 in words is "forty-five thousand, six hundred".