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.