Question

A six place number is formed by repeating a three place number; for example, $256,256or678,678$ etc. Any number of this form is always exactly divisible by:

• A. $7$ only
• B. $11$ only
• C. $13$ only
• D. $101$
• E. $1001$

Answer 1

The correct option is E $1001$

Such a number can be written as P. ${10}^3+P=P({10}^3+1)=P\left(1001\right)$, where P is the block of three digits that repeats. $\therefore$ (e) is the correct choice