78672 has 40 divisors (see below), whose sum is σ = 223200. Its totient is φ = 23680.

The previous prime is 78653. The next prime is 78691. The reversal of 78672 is 27687.

It is an interprime number because it is at equal distance from previous prime (78653) and next prime (78691).

It is a congruent number.

It is an inconsummate number, since it does not exist a number n which divided by its sum of digits gives 78672.

It is an unprimeable number.

78672 is an untouchable number, because it is not equal to the sum of proper divisors of any number.

It is a pernicious number, because its binary representation contains a prime number (7) of ones.

It is a polite number, since it can be written in 7 ways as a sum of consecutive naturals, for example, 454 + ... + 602.

It is an arithmetic number, because the mean of its divisors is an integer number (5580).

2⁷⁸⁶⁷² 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 78672, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (111600).

78672 is an abundant number, since it is smaller than the sum of its proper divisors (144528).

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

78672 is a wasteful number, since it uses less digits than its factorization.

78672 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 171 (or 165 counting only the distinct ones).

The product of its digits is 4704, while the sum is 30.

The square root of 78672 is about 280.4852937321. The cubic root of 78672 is about 42.8489381119.

It can be divided in two parts, 786 and 72, that added together give a palindrome (858).

The spelling of 78672 in words is "seventy-eight thousand, six hundred seventy-two".