• 648 is the smallest number that cannot be obtained by concatenating the absolute differences of adjacents digits of a larger number. For example, 647 can be obtained from 9370, because |9-3| = 6, |3-7| = 4, and |7-0| = 7.

• 648 can be written using four 4's:

648 has 20 divisors (see below), whose sum is σ = 1815. Its totient is φ = 216.

The previous prime is 647. The next prime is 653. The reversal of 648 is 846.

It is a powerful number, because all its prime factors have an exponent greater than 1 and also an Achilles number because it is not a perfect power.

648 is an esthetic number in base 8, because in such base its adjacent digits differ by 1.

It can be written as a sum of positive squares in only one way, i.e., 324 + 324 = 18^2 + 18^2 .

It is an ABA number since it can be written as A⋅B^{A}, here for A=3, B=6.

It is a Smith number, since the sum of its digits (18) coincides with the sum of the digits of its prime factors.

It is a Harshad number since it is a multiple of its sum of digits (18).

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

It is one of the 548 Lynch-Bell numbers.

It is a plaindrome in base 13, base 14 and base 16.

It is a nialpdrome in base 3, base 6 and base 9.

It is a zygodrome in base 3.

It is a self number, because there is not a number *n* which added to its sum of digits gives 648.

It is not an unprimeable number, because it can be changed into a prime (641) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (3) of ones.

It is a polite number, since it can be written in 4 ways as a sum of consecutive naturals, for example, 215 + 216 + 217.

2^{648} is an apocalyptic number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 648

648 is an abundant number, since it is smaller than the sum of its proper divisors (1167).

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

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

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

The sum of its prime factors is 18 (or 5 counting only the distinct ones).

The product of its digits is 192, while the sum is 18.

The square root of 648 is about 25.4558441227. The cubic root of 648 is about 8.6534974218.

Adding to 648 its sum of digits (18), we get a palindrome (666).

Subtracting from 648 its sum of digits (18), we obtain a triangular number (630 = T_{35}).

Multiplying 648 by its sum of digits (18), we get a square (11664 = 108^{2}).

648 divided by its sum of digits (18) gives a triangular number (36 = T_{8}).

It can be divided in two parts, 64 and 8, that multiplied together give a 9-th power (512 = 2^{9}).

The spelling of 648 in words is "six hundred forty-eight", and thus it is an aban number.

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