3648 has 28 divisors (see below), whose sum is σ = 10160. Its totient is φ = 1152.

The previous prime is 3643. The next prime is 3659. The reversal of 3648 is 8463.

3648 is nontrivially palindromic in base 7.

It is a nude number because it is divisible by every one of its digits.

It is one of the 548 Lynch-Bell numbers.

Its product of digits (576) is a multiple of the sum of its prime divisors (24).

It is a plaindrome in base 14 and base 15.

It is a nialpdrome in base 4, base 8 and base 16.

It is a zygodrome in base 15.

It is an inconsummate number, since it does not exist a number n which divided by its sum of digits gives 3648.

It is not an unprimeable number, because it can be changed into a prime (3643) by changing a digit.

3648 is an untouchable number, because it is not equal to the sum of proper divisors of any number.

It is a polite number, since it can be written in 3 ways as a sum of consecutive naturals, for example, 183 + ... + 201.

2³⁶⁴⁸ is an apocalyptic number.

3648 is a gapful number since it is divisible by the number (38) 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 3648, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (5080).

3648 is an abundant number, since it is smaller than the sum of its proper divisors (6512).

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

3648 is a wasteful number, since it uses less digits than its factorization.

3648 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 34 (or 24 counting only the distinct ones).

The product of its digits is 576, while the sum is 21.

The square root of 3648 is about 60.3986754822. The cubic root of 3648 is about 15.3940045251.

Adding to 3648 its product of digits (576), we get a palindrome (4224).

It can be divided in two parts, 36 and 48, that multiplied together give a cube (1728 = 12³).

The spelling of 3648 in words is "three thousand, six hundred forty-eight".