# Python Program for Check if all digits of a number divide it

Given a number n, find whether all digits of n divide it or not.
Examples:

Input : 128
Output : Yes
128 % 1 == 0, 128 % 2 == 0, and 128 % 8 == 0.

Input : 130
Output : No

We want to test whether each digit is non-zero and divides the number. For example, with 128, we want to test d != 0 && 128 % d == 0 for d = 1, 2, 8. To do that, we need to iterate over each digit of the number.

## python3

 `# Python 3 program to` `# check the number is` `# divisible by all ` `# digits are not.`   `# Function to check ` `# the divisibility ` `# of the number by` `# its digit.` `def` `checkDivisibility(n, digit) :` `    `  `    ``# If the digit divides the` `    ``# number then return true` `    ``# else return false.` `    ``return` `(digit !``=` `0` `and` `n ``%` `digit ``=``=` `0``)` `    `  `# Function to check if` `# all digits of n divide` `# it or not` `def` `allDigitsDivide( n) :` `    `  `    ``temp ``=` `n` `    ``while` `(temp > ``0``) :` `        `  `        ``# Taking the digit of` `        ``# the number into digit` `        ``# var.` `        ``digit ``=` `temp ``%` `10` `        ``if` `((checkDivisibility(n, digit)) ``=``=` `False``) :` `            ``return` `False`   `        ``temp ``=` `temp ``/``/` `10` `    `  `    ``return` `True`   `# Driver function` `n ``=` `128`   `if` `(allDigitsDivide(n)) :` `    ``print``(``"Yes"``)` `else` `:` `    ``print``(``"No"` `)` `    `  `# This code is contributed by Nikita Tiwari.`

Output

`Yes`

Time Complexity: O(log10n), where n represents the given integer.
Auxiliary Space: O(1), no extra space is required, so it is a constant.

Approach : Using str(),list(),map() and len() methods

## Python3

 `# Python 3 program to check the number is ` `# divisible by all digits are not.`   `n ``=` `128` `x ``=` `str``(n)` `a ``=` `list``(``map``(``int``, x))` `c ``=` `0` `for` `i ``in` `a:` `    ``if``(n ``%` `i ``=``=` `0``):` `        ``c ``+``=` `1` `if``(c ``=``=` `len``(a)):` `    ``print``(``"Yes"``)` `else``:` `    ``print``(``"No"``)`

Output

`Yes`

Time Complexity: O(nlogn)

Auxiliary Space: O(n)
Please refer complete article on Check if all digits of a number divide it for more details!

#### Approach#3: Using math

This approach is to factorize the number and check if each factor divides the number. If any factor of the number is not a digit or does not divide the number, then the answer is ‘No’. Otherwise, the answer is ‘Yes’.

#### Algorithm

1. Take the input number as n.
2. Factorize the number into a list of prime factors.
3. Traverse each factor of the number.
4. Check if the factor is a digit and divides the number.
5. If any factor is not a digit or does not divide the number, return ‘No’.
6. Otherwise, return ‘Yes’.

## Python3

 `from` `math ``import` `sqrt`   `def` `factorize(n):` `    ``factors ``=` `[]` `    ``while` `n ``%` `2` `=``=` `0``:` `        ``factors.append(``2``)` `        ``n ``=` `n ``/``/` `2` `    ``for` `i ``in` `range``(``3``, ``int``(sqrt(n)) ``+` `1``, ``2``):` `        ``while` `n ``%` `i ``=``=` `0``:` `            ``factors.append(i)` `            ``n ``=` `n ``/``/` `i` `    ``if` `n > ``2``:` `        ``factors.append(n)` `    ``return` `factors`   `def` `check_divide(n):` `    ``factors ``=` `factorize(n)` `    ``for` `factor ``in` `factors:` `        ``if` `factor < ``1` `or` `factor > ``9` `or` `n ``%` `factor !``=` `0``:` `            ``return` `'No'` `    ``return` `'Yes'` `n``=``128` `print``(check_divide(n))`

Output

`Yes`

Time Complexity: O(sqrt(n) log n), where n is the input number.
Auxiliary Space: O(sqrt(n)), where n is the input number.

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