• 40 can be written using four 4's:

•
A symmetric shape
tiled with the 40 *welded* polysticks of sizes 3, 4, and
5, i.e. those that contain at least a junction point:

• Deleting all the even digits from 2^{40} = 1099511627776 we obtain a prime (199511777).

40 has 8 divisors (see below), whose sum is σ = 90. Its totient is φ = 16.

The previous prime is 37. The next prime is 41. The reversal of 40 is 4.

40 is nontrivially palindromic in base 3, base 7 and base 9.

40 is an esthetic number in base 12, because in such base its adjacent digits differ by 1.

It can be written as a sum of positive squares in only one way, i.e., 36 + 4 = 6^2 + 2^2 .

It is a tau number, because it is divible by the number of its divisors (8).

40 is an admirable number.

It is a Harshad number since it is a multiple of its sum of digits (4).

It is a super Niven number, because it is divisible the sum of any subset of its (nonzero) digits.

40 is an idoneal number.

40 is a nontrivial repdigit in base 3, base 7 and base 9.

It is a plaindrome in base 3, base 7, base 9, base 11, base 12, base 14, base 15 and base 16.

It is a nialpdrome in base 3, base 4, base 7, base 8, base 9, base 10 and base 13.

It is a zygodrome in base 3, base 7 and base 9.

It is a panconsummate number.

It is a nontrivial repunit in base 3.

It is a pernicious number, because its binary representation contains a prime number (2) of ones.

A polygon with 40 sides can be constructed with ruler and compass.

It is a polite number, since it can be written as a sum of consecutive naturals, namely, 6 + ... + 10.

40 is the 4-th octagonal number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 40, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (45).

40 is an abundant number, since it is smaller than the sum of its proper divisors (50).

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

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

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

The sum of its prime factors is 11 (or 7 counting only the distinct ones).

The product of its (nonzero) digits is 4, while the sum is 4.

The square root of 40 is about 6.3245553203. The cubic root of 40 is about 3.4199518934.

The spelling of 40 in words is "forty", and thus it is an aban number, an eban number, an iban number, and an uban number.

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