Nombres harshad (itératif)

Un entier naturel non nul $n$ est dit harshad, si $n$ est divisible par la somme des chiffres de $n$. Le nom de harshad a été donné par le mathématicien Dattatreya Ramachandra Kaprekar (1905 - 1986), il signifie "grande joie" en sanskrit.

On précise qu'un nombre entier $b$ est un « diviseur » de $a$ si le reste de la division euclidienne de $a$ par $b$ vaut $0$.

Par exemple $18$ est un nombre harshad car $1+8=9$ divise $18$. En effet $18 =2\times (1+8)+0$.

Le but est d'écrire une fonction permettant de déterminer si un nombre est un nombre harshad ou non. Mais avant cela, il faudra écrire une fonction qui fait la somme des chiffres d'un nombre.

Question 1 : somme des chiffres

Écrire une fonction itérative somme_chiffres qui prend en paramètre un entier positif n et qui renvoie la somme des chiffres de n. On n'utilisera que des opérations mathématiques. On s'interdira donc de convertir n en une chaîne de caractères.

Exemples

>>> somme_chiffres(8)
8
>>> somme_chiffres(18)
9
>>> somme_chiffres(409)
13

str et sum interdits

On interdit dans cet exercice d'utiliser str et sum.

Rappels sur la division euclidienne

Avec Python, on rappelle qu'il est possible de calculer le quotient d'un nombre n par 10 avec l'expression n // 10.

De même, l'expression n % 10 renvoie le reste de la division euclidienne de n par 10.

🐍 Console Python

>>> 409 % 10
9
>>> 409 // 10
40
>>> 40 % 10
0
>>> 40 // 10
4

Version videVersion à trous

Évaluations restantes : 10/10

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Évaluations restantes : 10/10

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Question 2 : nombres harshad

Vous devez écrire une fonction harshad prenant en paramètre un nombre entier strictement positif n et renvoyant True si n est un nombre harshad et False sinon.

Vous pouvez utiliser la fonction somme_chiffres même si vous n'avez pas réussi à traiter la question précédente. Cette fonction est chargée automatiquement pour cette question.

Tester si un nombre est divisible par un autre

On rappelle qu'un nombre $a$ est divisible par $b$ si le reste de la division euclidienne de $a$ par $b$ est 0.

Exemples

>>> harshad(18)
True
>>> harshad(72)
True
>>> harshad(11)
False

Évaluations restantes : 10/10

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