67872 has 48 divisors (see below), whose sum is σ = 205632. Its totient is φ = 19200.

The previous prime is 67867. The next prime is 67883. The reversal of 67872 is 27876.

It is a tau number, because it is divible by the number of its divisors (48).

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

It is an alternating number because its digits alternate between even and odd.

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 7 ways as a sum of consecutive naturals, for example, 622 + ... + 722.

It is an arithmetic number, because the mean of its divisors is an integer number (4284).

2⁶⁷⁸⁷² 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 67872, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (102816).

67872 is an abundant number, since it is smaller than the sum of its proper divisors (137760).

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

67872 is a wasteful number, since it uses less digits than its factorization.

67872 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 121 (or 113 counting only the distinct ones).

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

The square root of 67872 is about 260.5225518069. The cubic root of 67872 is about 40.7909245481.

It can be divided in two parts, 67 and 872, that added together give a palindrome (939).

The spelling of 67872 in words is "sixty-seven thousand, eight hundred seventy-two".