# Module that finds the sum of digits of any given positive integer

How can I make a module that finds the sum of digits of any given positive integer?

I use this command

F[x_]:= Apply[ Plus, IntegerDigits[x] ]


Is there another module to do it ?

• Total@IntegerDigits[x]
– Kuba
Dec 19, 2013 at 23:58
• Totlal work as plus ??
– rola
Dec 20, 2013 at 0:02
• @rola Look in the Mathematica documentation (F1 button in Mathematica), it is very useful. Total is basically the same as Plus @@ # & which is the same as Apply[Plus, #] &. The main difference, I suppose, is that Total allows you to specify the level (for example you can add up all the elements of a matrix, instead of its rows).
– amr
Dec 20, 2013 at 0:12
• @amr thank you.... but when I have to use module or block . I have to use it like g [n_]:=Module [ ] right!!
– rola
Dec 20, 2013 at 0:22
• Why do you "have to use Module or Block"? Dec 20, 2013 at 9:58

Mathematical v14.0 introduced DigitSum. For example:

DigitSum[2525]
(* 14 *)


DigitSum threads over lists.

DigitSum[{4397, 4268, 782, 2969, 4286}]
(* {23, 20, 17, 26, 20} *)


Find the same results with Total and IntegerDigits:

Total[IntegerDigits[2525]]
(* 14 *)

Total /@ IntegerDigits[{4397, 4268, 782, 2969, 4286}]
(* {23, 20, 17, 26, 20} *)


Yes, there are other ways. In Mathematica there are usually many other ways.

Here is a way using DigitCount and Dot:

f1[n_Integer] := DigitCount[n].{1,2,3,4,5,6,7,8,9,0}

f1[2147]

14


It can be easily extended to bases other than 10:

Clear[f1]

f1[n_Integer, b : (_Integer?Positive) : 10] := DigitCount[n, b].Mod[Range[b], b]


In base 7:

f1[2147, 7]

17


Note that there is no need to use Module (or Block), and in fact doing so for concise functions is needless clutter. Module should be used when you need localized Symbols, not merely as cruft to wrap every function you write. Block should be used even more selectively as it temporarily modifies global values. Please see: What are the use cases for different scoping constructs?

Also since I assume you are a new Mathematica user (and even if you're not) I recommend referencing What are the most common pitfalls awaiting new users?.

At some point you may wish to read How to Combine Pattern Constraints and Default Values for Function Arguments for an understanding of the second parameter pattern I used in the extended definition of f1.

Another way:

NumberDecompose[2525, {1000, 100, 10, 1}]//Total

(* 14 *)


Or

NumberDecompose[2525, {1000, 100, 10, 1}] // NumberCompose[#, {1, 1, 1, 1}] &

(* 14 *)

• f = Total@ NumberDecompose[#, Reverse@PowerRange[1, 10^Floor@Log10@#]] &;
– Syed
Mar 18 at 9:52
f = Total @ ToExpression @ DeleteCases["-"] @ Characters @ ToString @ # &;

f @ 2147


14

f /@ {-4, 0, 4, 44, 444}


{4, 0, 4, 8, 12}

dsum[n_] := Last@Accumulate[IntegerDigits[n]]


Test:

{#, dsum @#} & /@ RandomInteger[{500, 4000}, 5] // Column


f = # /. x_ :> Plus @@ ToExpression@Characters[ToString[Abs@x]] &;

f@2147


14

f /@ {-4, 0, 4, 44, 444}


{4, 0, 4, 8, 12}