72648 has 24 divisors (see below), whose sum is σ = 196950. Its totient is φ = 24192.

The previous prime is 72647. The next prime is 72649. The reversal of 72648 is 84627.

It is an interprime number because it is at equal distance from previous prime (72647) and next prime (72649).

It can be written as a sum of positive squares in only one way, i.e., 66564 + 6084 = 258^2 + 78^2 .

It is a tau number, because it is divible by the number of its divisors (24).

72648 is a modest number, since divided by 648 gives 72 as remainder.

It is an inconsummate number, since it does not exist a number n which divided by its sum of digits gives 72648.

It is not an unprimeable number, because it can be changed into a prime (72643) 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, 433 + ... + 576.

2⁷²⁶⁴⁸ is an apocalyptic number.

It is an amenable number.

72648 is an abundant number, since it is smaller than the sum of its proper divisors (124302).

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

72648 is a wasteful number, since it uses less digits than its factorization.

72648 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 1021 (or 1014 counting only the distinct ones).

The product of its digits is 2688, while the sum is 27.

The square root of 72648 is about 269.5329293426. The cubic root of 72648 is about 41.7261089362.

It can be divided in two parts, 72 and 648, that multiplied together give a 6-th power (46656 = 6⁶).

The spelling of 72648 in words is "seventy-two thousand, six hundred forty-eight".