40768 has 42 divisors (see below), whose sum is σ = 101346. Its totient is φ = 16128.

The previous prime is 40763. The next prime is 40771. The reversal of 40768 is 86704.

It can be written as a sum of positive squares in only one way, i.e., 28224 + 12544 = 168^2 + 112^2 .

It is a zygodrome in base 7.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (40763) by changing a digit.

40768 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 5 ways as a sum of consecutive naturals, for example, 3130 + ... + 3142.

It is an arithmetic number, because the mean of its divisors is an integer number (2413).

2⁴⁰⁷⁶⁸ is an apocalyptic number.

40768 is the 128-th heptagonal number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 40768, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (50673).

40768 is an abundant number, since it is smaller than the sum of its proper divisors (60578).

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

40768 is a wasteful number, since it uses less digits than its factorization.

40768 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 39 (or 22 counting only the distinct ones).

The product of its (nonzero) digits is 1344, while the sum is 25.

The square root of 40768 is about 201.9108714260. The cubic root of 40768 is about 34.4170097958.

It can be divided in two parts, 40 and 768, that added together give a palindrome (808).

The spelling of 40768 in words is "forty thousand, seven hundred sixty-eight".