# Python program to find better divisor of a number

PythonServer Side ProgrammingProgramming

Suppose we have a number n. We have to find divisor of n which one is better based on these conditions: We have two numbers p and q, the one whose digits sum to a larger number is called better than the other one. When the sum of digits is same, then the smaller number is the better one.

So, if the input is like n = 180, then the output will be 9 because the divisors are [1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, 180]. So the number whose digit sums are maximum are [9, 18, 36, 45, 90, 180], but among them 9 is better number as its value is smaller.

To solve this, we will follow these steps −

• div := 1, md := 1
• for i in range 2 to n, do
• k := i
• if n mod i > 0, then
• go for next iteration
• s := 0
• while k > 0, do
• s := s + k mod 10
• k := k / 10
• if s > md, then
• md := s
• div := i
• return div

## Example

Let us see the following implementation to get better understanding

def solve(n):
div = 1
md = 1
for i in range(2, n + 1):
k = i
if n % i > 0:
continue
s = 0
while k > 0:
s += k % 10
k /= 10
if s > md:
md = s
div = i

return div

n = 180
print(solve(n))

## Input

180


## Output

9