It has an aliquot sum of 7 in the 4 member aliquot sequence (8,7,1,0) being the first member of 7-aliquot tree. All powers of 2 (2^x), have an aliquot sum of one less than themselves.

A number is divisible by 8 if its last 3 digits, when written in decimal, are also divisible by 8, or its last 3 digits are 0 when written in binary.

8 and 9 form a Ruth–Aaron pair under the second definition in which repeated prime factors are counted as often as they occur.

There are a total of eight convex deltahedra.

A polygon with eight sides is an octagon. Figurate numbers representing octagons (including eight) are called octagonal numbers.

A polyhedron with eight faces is an octahedron. A cuboctahedron has as faces six equal squares and eight equal regular triangles.

A cube has eight vertices.

Sphenic numbers always have exactly eight divisors.

The number 8 is involved with a number of interesting mathematical phenomena related to the notion of Bott periodicity. For example, if O(∞) is the direct limit of the inclusions of real orthogonal groups

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