Check if N is divisible by a number which is composed of the digits from the set {A, B} in Python

Suppose we have a number n. We have another two numbers a and b. We have to check whether we can generate a number using a and b that divides n.

So, if the input is like n = 115, a = 3, b = 2, then the output will be True as 115 is divisible by 23 which is made of 2 and 3.

To solve this, we will follow these steps −

• Define a function util() . This will take temp, a, b, n
• if temp > n, then
  • return False

• if n is divisible by temp, then

  • return True
• return true when at least one of util(temp * 10 + a, a, b, n) or util(temp * 10 + b, a, b, n) is true otherwise false
• From the main method return true when at least one of util(a, a, b, n) or util(b, a, b, n) is true otherwise false

Example

Let us see the following implementation to get better understanding −

 Live Demo

def util(temp, a, b, n):
   if temp > n:
      return False
   if n % temp == 0:
      return True
   return util(temp * 10 + a, a, b, n) or util(temp * 10 + b, a, b, n)
def solve(n, a, b):
   return util(a, a, b, n) or util(b, a, b, n)
n = 115
a = 3
b = 2
print(solve(n, a, b))

Input

115, 2, 3

Output

True