42768 has 60 divisors (see below), whose sum is σ = 135408. Its totient is φ = 12960.

The previous prime is 42767. The next prime is 42773. The reversal of 42768 is 86724.

It is a Harshad number since it is a multiple of its sum of digits (27).

Its product of digits (2688) is a multiple of the sum of its prime divisors (16).

It is a nialpdrome in base 6 and base 16.

It is not an unprimeable number, because it can be changed into a prime (42767) by changing a digit.

It is a polite number, since it can be written in 11 ways as a sum of consecutive naturals, for example, 3883 + ... + 3893.

2⁴²⁷⁶⁸ is an apocalyptic number.

42768 is a gapful number since it is divisible by the number (48) 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 42768, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (67704).

42768 is an abundant number, since it is smaller than the sum of its proper divisors (92640).

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

42768 is a wasteful number, since it uses less digits than its factorization.

42768 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 34 (or 16 counting only the distinct ones).

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

The square root of 42768 is about 206.8042552754. The cubic root of 42768 is about 34.9708600995.

Subtracting 42768 from its reverse (86724), we obtain a triangular number (43956 = T₂₉₆).

It can be divided in two parts, 4 and 2768, that added together give a palindrome (2772).

The spelling of 42768 in words is "forty-two thousand, seven hundred sixty-eight".