Residue of a natural entirety

See also: Residue

The residue (or numerical root ) of a natural entirety is the Nombre obtained by adding all its Chiffre S, then by adding the figures with the result, and so on until obtaining a number with only one figure.

For example, the residue of number 65.536 is 7 because 6 + 5 + 5 + 3 + 6 = 25, then 2 + 5 = 7.

In particular cases, the residue of an entirety takes well defined values.

the residue of a square perfect is 1,4,7, or 9.
the residue of a Prime number (except for 3) is 1,2,4,5,7, or 8.
the residue of a power of 2 is 1,2,4,5,7, or 8.
the residue of a Perfect number (except 6) is 1.
the residue of a spangled Nombre is 1 or 4.

The residues can be calculated using the Congruence S rather than by the addition of all the figures. Indeed, if one considers the remainder N of the Euclidean Division of NR by 9 (i.e. NR is adequate with N modulo 9):

if N = 0, the residue of NR is 9
if not, the residue of NR is N .

The residues of entireties can be used like Somme of control.

One can also quote some Pseudo-science S such as the Numérologie which usually appeal there; to see the article recursive Numerology with 9 numbers.

See too

Persistence of a number

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