Question

When a certain number is multiplied by $13$ , the product consists entirely of fives .The smallest such number is _____ .

• A. $41625$
• B. $42515$
• C. $42735$
• D. $42135$

Answer 1

Answer: (C)

$42735$

By hit and trial, we find that a number exactly divisible by $13$ and consisting entirely of five's is $555555$.
On dividing $555555$ by $13$, we get

$42735$ as a quotient.

Thus the required number is $42735$.