MathDB

For a positive integer

n

, we consider all its divisors (including

1

and itself). Suppose that

p\%

of these divisors have their unit digit equal to

3

. (For example

n = 117

, has six divisors, namely

1,3,9,13,39,117

. Two of these divisors namely

3

and

13

, have unit digits equal to

3

. Hence for

n = 117

p =33.33...

). Find, when

n

is any positive integer, the maximum possible value of

p

Problem Statement