• 10 can be written using four 4's:

• H. Harborth proved that, given 10 points in general position, there are always five of them which are the corners of a convex pentagon that does not contain any of the remaining points.

• Marion's theorem states that the area of the central hexagon determined by trisecting each side of a triangle and connecting the points as shown below, is 1/10 of the area of the triangle.

10 has 4 divisors (see below), whose sum is σ = 18. Its totient is φ = 4.

The previous prime is 7. The next prime is 11.

10 = T_{1} + T_{2} +
T_{3}.

It is a happy number.

10 is nontrivially palindromic in base 3, base 4 and base 9.

10 is digitally balanced in base 2, because in such base it contains all the possibile digits an equal number of times.

It is a Cunningham number, because it is equal to 3^{2}+1.

10 is an esthetic number in base 2, base 3, base 8 and base 10, because in such bases its adjacent digits differ by 1.

10 is a nontrivial binomial coefficient, being equal to C(5, 2).

It is a semiprime because it is the product of two primes, and also a brilliant number, because the two primes have the same length, and also an emirpimes, since its reverse is a distinct semiprime: 1 = 7883958449819444595 ⋅7733349.

It can be written as a sum of positive squares in only one way, i.e., 9 + 1 = 3^2 + 1^2 .

It is a Harshad number since it is a multiple of its sum of digits (1).

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

10 is an idoneal number.

10 is an undulating number in base 2 and base 3.

It is the 8-th Perrin number.

10 is a nontrivial repdigit in base 4 and base 9.

It is a plaindrome in base 4, base 6, base 7, base 8 and base 9.

It is a nialpdrome in base 4, base 5, base 9 and base 10.

It is a zygodrome in base 4 and base 9.

It is a panconsummate number.

It is the 3-rd tetrahedral number.

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

A polygon with 10 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, 1 + ... + 4.

10 is the 4-th triangular number and also the 2-nd decagonal number.

10 is the 3-rd centered triangular number and also the 2-nd centered nonagonal number.

10 is a deficient number, since it is larger than the sum of its proper divisors (8).

10 is an equidigital number, since it uses as much as digits as its factorization.

With its predecessor (9) it forms an eRAP, since the sums of their prime factors are consecutive (6 and 7).

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

The sum of its prime factors is 7.

The product of its (nonzero) digits is 1, while the sum is 1.

The square root of 10 is about 3.1622776602. The cubic root of 10 is about 2.1544346900.

The spelling of 10 in words is "ten", and thus it is an aban number, an iban number, an oban number, and an uban number.

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