45648 has 30 divisors (see below), whose sum is σ = 128154. Its totient is φ = 15168.

The previous prime is 45641. The next prime is 45659. The reversal of 45648 is 84654.

It can be written as a sum of positive squares in only one way, i.e., 28224 + 17424 = 168^2 + 132^2 .

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (45641) by changing a digit.

It is a polite number, since it can be written in 5 ways as a sum of consecutive naturals, for example, 15 + ... + 302.

2⁴⁵⁶⁴⁸ is an apocalyptic number.

45648 is a gapful number since it is divisible by the number (48) 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 45648, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (64077).

45648 is an abundant number, since it is smaller than the sum of its proper divisors (82506).

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

45648 is a wasteful number, since it uses less digits than its factorization.

45648 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 331 (or 322 counting only the distinct ones).

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

The square root of 45648 is about 213.6539257772. The cubic root of 45648 is about 35.7388509091.

The spelling of 45648 in words is "forty-five thousand, six hundred forty-eight".